In the four hundred and eightieth year after the children of Israel came out of the land of Egypt, in the fourth year of Solomon’s reign over Israel, in the month Ziv (which is the second month), he began to build the house of the Lord.
-1 Kings 6:1
In First Kings, scripture reckons the start of the fourth year of Solomon's reign, when he began building the temple. So, the 480 years covers the time from the Exodus through the third year of Solomon's reign (the fourth year having just begun, but not completed).
Some have tried to argue that this is in contradiction to what Paul states in Acts chapter 13. Now, Israel is God's timepiece from the time of Abraham to the start of the current age (Post Acts) and will soon be again. God is not done with Israel and he will fulfill all his promises to the nation in an age to come.
So, let's look at Paul's timetable in Acts 13.
Then Paul stood up, and motioning with his hand said: “Men of Israel, and you who fear God, listen. The God of this people of Israel chose our fathers, and exalted the people when they lived as foreigners in the land of Egypt, and with great power He led them out of it. For about forty years He endured their conduct in the desert. When He had destroyed seven nations in the land of Canaan, He gave them their land as an inheritance by lot. “After about four hundred and fifty years, God gave them judges until Samuel the prophet. Then they requested a king. And God gave them Saul the son of Kish, a man of the tribe of Benjamin, for forty years. When He had removed him, He raised up David to be their king, of whom He testified, saying, ‘I have found David the son of Jesse, a man after My own heart, who will fulfill My entire will.’
-Acts 13:17-22
Here we have 40 years in the desert. Then we have another 450 years of the time of the judges until Samuel. Then 40 years of Saul, 40 years of David, add the three years into Solomon's reign to start building the temple. This gives us 573 years from the exodus from Egypt to Solomon and the temple as noted in 1 Kings 6.
How do we explain the seeming 93 year discrepancy?
We first have to turn to the prophet Hosea.
Then the Lord said: “Call his name Lo-Ammi, for you are not My people, and I am not your God.”
-Hosea 1:9
During Israel's history, there are periods during which God pictures them as "not My people." Of course, Paul reckons all the time from the Exodus to Solomon as Israel's history. We see that while God may put up a parenthesis in His dealings with Israel, when it comes to the earthly plan and hope, Israel (the seed of Abraham) is still at the center of God's plan.
So where are the missing 93 years? They're in the Book of Judges during times Israel was "Lo-Ammi" or "not My people."
The children of Israel did what was evil in the sight of the Lord. They forgot the Lord their God and served the Baals and the Asherahs. The anger of the Lord burned against Israel, and He sold them into the hands of Cushan-Rishathaim, king of Mesopotamia. The children of Israel served Cushan-Rishathaim for eight years.
-Judges 3:7-8
Then the children of Israel once more did what was evil in the sight of the Lord... The children of Israel served King Eglon of Moab for eighteen years.
-Judges 3:12,14
When Ehud was dead, the children of Israel once more did what was evil in the sight of the Lord. The Lord sold them into the hands of King Jabin of Canaan, who ruled in Hazor. The commander of his army was Sisera. He lived in Harosheth Haggoyim. The children of Israel cried out to the Lord, for Sisera had nine hundred iron chariots and had forcefully oppressed the children of Israel for twenty years.
-Judges 4:1-4
The children of Israel did evil in the sight of the Lord, so the Lord gave them into the hands of Midian for seven years.
-Judges 6:1
Again the children of Israel did evil in the sight of the Lord, so the Lord gave them into the hands of the Philistines for forty years.
-Judges 13:1