Timeline difficulty

In the four hundred and eightieth year after the Israelites came out of Egypt, in the fourth year of Solomon's reign over Israel, in the month of Ziv, the second month, he began to build the temple of the LORD. (1 Kings 6:1)

Solomon reigned around the year 970 as king. This would mean the Torah was given to the Israelites in 1450 BC. According to the Bible Moses was 80 years old when he was send to Pharaoh, give or take a few years we can assume from 1 Kings 6:1 dates Moses would have been born around 1530. The Exodus in the 13th century BC are the mention of the city of Rameses in Exodus 1:11 and the destruction of Hazor recorded in Joshua 11:11.

In Exodus we read:

So they put slave masters over them to oppress them with forced labor, and they built Pithom and Rameses as store cities for Pharaoh. (Exodus 1:11)

As mentioned above, the ancient city of Rameses built by Rameses the Great (Rameses II) is well known from Egyptian records and archaeological excavation. Thus, it is presumed that the Israelites helped build Rameses II’s capital city and that they were still in Egypt in the 13th century BC. Since we know from the Merenptah, or Israel, Stela that Israel was in Canaan early in the reign of Rameses II’s son Merenptah, ca. 1220 BC (Wood 2005a), the Exodus must have taken place 40 years or more prior to that, during the reign of Rameses II. This particular theory has gained favor with many scholars and, as a result, Rameses II is the Pharaoh of the Exodus in Hollywood and the popular media. There are, however, insurmountable obstacles associated with this reconstruction.

Here's the problem, The predominant view of modern scholarship is that the Pharaoh of the Exodus was Ramses II. If this is right, it would mean that the Exodus took place about 1270 to 1260 b.c. However, since the fourth year of Solomon’s reign was 967 b.c., adding 480 years to that date would put the Exodus at about 1447 b.c. which is in the reign of Amenhotep II. How can this calculation be correct if Ramses the Great was the Pharaoh of the Exodus?

this timeline error is also recognised by biblical commentators

Ellicott's Commentary for English Readers

(1) In the fourth year.--This date, given with marked precision, forms a most important epoch in the history of Israel, on which, indeed, much of the received chronology is based. In the LXX., 440 is read for 480, possibly by an interchange of two similar Hebrew letters, or, perhaps, by reckoning from the completion of Exodus at the death of Moses instead of its beginning. The Vulgate agrees with the Hebrew text. Josephus, on the other hand, without any hint of any other reckoning in the Scriptural record, gives 592 years. The date itself, involving some apparent chronological difficulties, has been supposed to be an interpolation; but without any sufficient ground, except Josephus's seeming ignorance of its existence, and some early quotations of the passage by Origen and others without it; and in neglect of the important fact that, disagreeing prima facie with earlier chronological indications in Scripture, it is infinitely unlikely to have been thus interpolated by any mere scribe.

These indications are, however, vague. The period includes the conquest and rule of Joshua, the era of the Judges down to Samuel, the reigns of Saul and David, and the three years of Solomon's reign already elapsed. Now, of these divisions, only the last three can be ascertained with any definiteness, at about 83 years. The time occupied by the conquest and rule of Joshua, cannot be gathered with any certainty from Scripture. The same is the case with the duration of some of the subsequent Judgeships. Even the numerous chronological notices given in the Book of Judges are inconclusive. We cannot tell whether they are literally accurate, or, as the recurrence of round numbers may seem to suggest..

Pulpit Commentary

Verse 1. - And it came to pass in the four hundred and eightieth year after the children of Israel were come out of the land of Egypt[This date has been the subject of much controversy, which cannot even now be considered (pace Keil: "The correctness of the number 480 is now pretty generally admitted") as closed. Grave doubts are entertained as to its genuineness. Lord A. Hervey (Dict. Bib. vol. 2. p. 22) says it is "manifestly erroneous." Rawlinson considers it to be "an interpolation into the sacred text" (p. 515). And it is to he observed, 
1. that the LXX. reads 440 instead of 480 years - a discrepancy which is suspicious, and argues some amount of incertitude. 
2. Origen quotes this verse without these words (Comm. in S. Johann 2:20). 
3. They would seem to have been unknown to Josephus, Clem. Alex., and others. 
4. It is not the manner of Old Testament writers thus to date events from an era, an idea which appears to have first occurred to the Greeks temp. Thucydides (Rawlinson). It is admitted that we have no other instance in the Old Testament where this is done. 
5. It is difficult to reconcile this statement with other chronological notices both of the Old and New Testaments. For taking the numbers which we find in the Hebrew text of the books which refer to this period, they sum up to considerably more than 480 years. The time of the Judges alone comprises 410 years at the least. It should be stated, however, with regard to the chronology of the period last mentioned 
(1) that it only pretends to furnish round numbers - 20, 40, and the like - and evidently does not aim at exactitude; 

Cambridge Bible for Schools and Colleges

Ch. 1 Kings 6:1-10. Commencement and dimensions of Solomon’s Temple (2 Chronicles 3:1-2)
1. in the four hundred and eightieth year, &c.] It is impossible to discover how this date is arrived at, or to make it fit in with other statements of the Old and New Testament. The LXX. has ‘the four hundred and fortieth year’, and Josephus ‘the five hundred and ninety’

second.’ If we put together the numbers which we find in the Old Testament record, we have 40 years between the Exodus and the death of Moses, 40 years peace after Othniel, 80 after Ehud; Jabin’s oppression lasted 20 years, there were 40 years of peace after Barak, 40 in Gideon’s time: Tola judged the land 23 years, Jair 22, Jephthah 6, Ibzan 7, Elon 10, Abdon 8: the servitude to the Philistines lasted 40 years, and Samson judged 20 years. After this we have as dates Eli 40 years, Samuel 20 (1 Samuel 7:2) at least, David 40, Solomon 4. These make a total of 498. But we cannot be sure that some of these judgeships were not contemporary with or overlapping one another, 

What was the length of time that the Israelites lived in Egypt?

Masoretic Torah (Egypt only) 430 years.

Samaritan Torah both (Egypt & Canaan) 430 years.

1 Kings 6:1 (Egypt only ) 480 years

LXX 1 Kings 6:1 (Egypt only 440 years

Book of Jubilees (Egypt only) 400 years

What a mess!