For the Scripture says, “Whoever believes in Him will not be ashamed.” For there is no distinction between Jew and Greek, for the same Lord over all is generous toward all who call upon Him. For, “Everyone who calls on the name of the Lord shall be saved.”
-Romans 10:11-13
The invisible things about Him—His eternal power and deity—have been clearly seen since the creation of the world and are understood by the things that are made, so that they are without excuse.
-Romans 1:20
How then shall they call on Him in whom they have not believed? And how shall they believe in Him of whom they have not heard? And how shall they hear without a preacher? And how shall they preach unless they are sent? As it is written: “How beautiful are the feet of those who preach the gospel of peace, who bring good news of good things!"
-Romans 10:14-15
But they have not all obeyed the gospel. For Isaiah says, “Lord, who has believed our [Israel's] report?” So then faith comes by hearing, and hearing by the word of God. But I say, have they not heard? Yes, indeed:
“Their voice went into all the earth,
and their words to the ends of the world...
-Romans 10:16-18
What advantage then does the Jew have? Or what profit is there in circumcision? Much in every way! Chiefly because the oracles of God were entrusted to them [the Jews].
-Romans 3:1-2
Then Paul stood in the middle of the Areopagus, and said: “Men of Athens, I perceive that in all things you are very religious. For as I passed by and looked up at your objects of worship, I found an altar with this inscription: TO THE UNKNOWN GOD. Whom you therefore unknowingly worship, Him I proclaim to you. “God who made the world and all things in it, being Lord of heaven and earth, does not live in temples made by hands. Nor is He served by men’s hands, as though He needed anything, since He gives all men life and breath and all things. He has made from one blood every nation of men to live on the entire face of the earth, having appointed fixed times and the boundaries of their habitation, that they should seek the Lord so perhaps they might reach for Him and find Him, though He is not far from each one of us. ‘For in Him we live and move and have our being.’ As some of your own poets have said, ‘We are His offspring.’ “Therefore since we are the offspring of God, we ought not to suppose that the Deity is like gold or silver or stone or an engraved work of art or an image of the reflection of man. God overlooked the times of ignorance, but now He commands all men everywhere to repent. For He has appointed a day on which He will judge the world in righteousness by a Man whom He has appointed, having given assurance of this to all men by raising Him from the dead.”
-Acts 17:22-31
And as the sailors were seeking to escape from the ship, when they had let down the skiff into the sea, under pretense of putting out anchors from the prow, Paul said to the centurion and the soldiers, “Unless these men stay in the ship, you cannot be saved.”
-Acts 27:30-31
But I say, did Israel not know? First, Moses says:
“I will make you [Israel] jealous by those who are not a nation,
and by a foolish nation I will anger you.”
-Romans 10:19
And Isaiah is very bold and says:
“I was found by those who did not seek Me;
I revealed myself to those who did not ask for Me.”[Isaiah 65:1]But to Israel He says:
“All day long I have stretched out My hands
to a disobedient and contrary people.”[Isaiah 65:2]
-Romans 10:20-21
Moses went up to God, and the Lord called to him from the mountain, saying, “Thus you shall say to the house of Jacob and tell the children of Israel: You have seen what I did to the Egyptians, and how I lifted you up on eagles’ wings, and brought you to Myself. Now therefore, if you will faithfully obey My voice and keep My covenant, then you [Israel] shall be My special possession out of all the nations, for all the earth is Mine. And you will be to Me a kingdom of priests and a holy nation.’ These are the words which you shall speak to the children of Israel.”
-Exodus 19:3-6
For I, the Lord, love justice,
I hate robbery in the burnt offering;
and I will faithfully give them their recompense
and make an everlasting covenant with them.
Their descendants shall be known among the Gentiles
and their offspring among the peoples.
All who see them shall acknowledge them
because they are the descendants whom the Lord has blessed.
-Isaiah 61:8-9
When they had traveled through Amphipolis and Apollonia, they came to Thessalonica, where there was a synagogue of the Jews. According to his custom, Paul went in, and on three Sabbaths he lectured to them from the Scriptures, explaining and proving that the Christ had to suffer and to rise from the dead, and saying, “This Jesus, whom I preach to you, is the Christ.” Some of them were persuaded and joined with Paul and Silas, including a great crowd of devout Greeks and many leading women.
-Acts 17:1-4
Philip found Nathanael and said to him, “We have found Him of whom Moses in the law, as well as the prophets, wrote, Jesus of Nazareth, the son of Joseph.”
-John 1:45
“Do not think that I shall accuse you to the Father. There is one who accuses you—Moses, in whom you [Israel] trust. For if you believed Moses, you would believe Me, for he wrote of Me. But if you do not believe his writings, how will you believe My words?”
-John 5:45-57
Therefore having obtained help from God, I continue to this day, testifying both to small and great, saying nothing but what the prophets and Moses said would happen
-Acts 26:22
As we continue in Romans 10, Paul again turns to the prophet Isaiah.
And Isaiah is very bold and says:
“I was found by those who did not seek Me;
I revealed myself to those who did not ask for Me.”
-Romans 10:20
“I was sought by those who did not ask for Me;
I was found by those who did not seek Me.
I said, ‘Here I am, here I am,’ To a nation that was not called by My name.
I have spread out My hands all day
to a rebellious people [Israel]
who walk in a way that was not good,
after their own thoughts
But to Israel [alone] He says:
“All day long I have stretched out My hands
to a disobedient and contrary people.”
-Romans 10:21
We remember that Paul was utterly clear in Romans 9 to whom [present tense at the time of the writing of Romans] God entrusted his earthly calling.
I am speaking the truth in Christ, I am not lying; my conscience testifies with me in the Holy Spirit, that I have great sorrow and continual anguish in my heart. For I could wish that I myself were accursed from Christ for my brothers, my kinsmen by race, who are Israelites, to whom belong the adoption, the glory, the covenants, the giving of the law, the service of God, and the promises, to whom belong the patriarchs, and from whom, according to the flesh, is Christ, who is over all, God forever blessed. Amen.
-Romans 9:1-5
When we see the distinctions and lines that God has drawn and which scripture rightly divided reveals, we can see the full argument Paul is making.
How then shall they [Gentiles] call on Him in whom they have not believed? And how shall they believe in Him of whom they have not heard? And how shall they hear without a preacher?...
So then faith comes by hearing, and hearing by the word of God. But I say, have they not heard? Yes, indeed:
“Their voice went into all the earth,
and their words to the ends of the world...
Israel was called to be the witness to the nations. They failed in that calling. But when Paul asks if "they" have heard and quotes Palm 19:4. We must note, from the full context (that a Jew would know) that the "they" that have heard are gentile nations and the "they/their" speaking and proclaiming and voicing are the heavens and the skies (i.e. Creation).
The heavens declare the glory of God;
the skies proclaim the work of his hands.
Day after day they pour forth speech;
night after night they reveal knowledge.
They have no speech, they use no words;
no sound is heard from them.
Yet their voice goes out into all the earth,
their words to the ends of the world.
-Psalm 19:1-4
The argument Paul is making in Romans 10:14-15 is not that the missions committee needs to raise funds for missionaries (although there is nothing wrong with that), but rather that while Israel failed in her calling to witness to the nations, God did not the fail the nations as they have creation witnessing to them.
Paul asks, "have they not heard?" and he emphatically points to scripture to say that even without human voices, even in Israel's failure, "yes indeed" the nations have heard.
In the Acts, God offered "the restoration of the Kingdom in Israel" (Acts 1) and "the restoration of all things" (Acts 3) to Israel if she repented. When she failed to listen, God grafted in Gentiles into the promises in the Kingdom for the sole purpose of making Israel jealous. When none of this worked, God revealed a new heavenly plan to Paul in the Book of Ephesians and put the earthly plan on hold.
[The risen Lord Jesus] presented Himself alive after His passion by many infallible proofs, appearing to them for forty days, and speaking concerning the kingdom of God. Being assembled with them, He commanded them, “Do not depart from Jerusalem, but wait for the promise of the Father, of which you have heard from Me. For John baptized with water, but you shall be baptized with the Holy Spirit not many days from now.” So when they had come together, they asked Him, “Lord, will You at this time restore the kingdom to Israel?”
-Acts 1:3-6
“Now brothers [Men of Israel, v.12] , I know that you acted in ignorance, as did also your rulers. But what God foretold through all the prophets, that His Christ should suffer, He thus fulfilled. Therefore repent and be converted, that your sins may be wiped away, that times of refreshing may come from the presence of the Lord, and that He may send the One who previously was preached to you, Jesus Christ, whom the heavens must receive until the time of restoring all things which God spoke through all His holy prophets since the world began.
-Acts 3:17-21
For this cause I Paul, the prisoner of Jesus Christ for you Gentiles, if you have heard of the dispensation of the grace of God which is given me to you-ward: how that by revelation he made known unto me the mystery; (as I wrote afore in few words, whereby, when you read, you may understand my knowledge in the mystery of Christ) which in other ages was not made known unto the sons of men, as it is now revealed unto his holy apostles and prophets by the Spirit; that the Gentiles should be fellowheirs, and of the same body, and partakers of his promise in Christ by the gospel: whereof I was made a minister, according to the gift of the grace of God given unto me by the effectual working of his power.
-Ephesians 3:1-7 [this is not part of the earthly plan, but of the current heavenly calling]
Romans 10 is not about the missionary committee. It is part of Paul's argument for the calling of the Gentiles into the earthly promises to Israel for the purpose of making Israel jealous. The goal is to bring Israel to repentance so she can take her place in the earthly plan of God. That repentance is yet future and part of an age to come.
Paul is telling Jews that despite their disobedience, God has reached the Gentiles. They have heard.
And how shall they believe in Him of whom they have not heard?... But I say, have they not heard? Yes, indeed...
But I say, did Israel not know? First, Moses says: “I will make you [Israel] jealous by those who are not a nation, and by a foolish nation I will anger you.”
-Romans 10:19
I say then, have they [Israel] stumbled that they should fall? God forbid! But through their transgression salvation has come to the Gentiles, to make them [Israel] jealous.
-Romans 11:11
For I am speaking to you Gentiles. Inasmuch as I am the apostle to the Gentiles, I magnify my ministry, if somehow I may make my kinsmen [Jews] jealous and may save some of them. For if their rejection means the reconciliation of the world, what will their acceptance mean but life from the dead?
-Romans 11:13-15
Israel's acceptance will come. But only after the current age ends and only after her time of testing and cleansing. This is all part of the Plan for the Earth.