I think that, as always, we should be a bit cautious about declaring archaeological discoveries as “proof” of biblical statements, but the Soleb Inscription appears to offer some of the best potential support to the Old Testament narrative that we have. This inscription comes from the far South of Egypt, in Nubia, which is the far North of Sudan today. In this inscription from somewhere very close to 1400 BC Pharaoh Amenhotep III claims to have conquered a people he calls the Shashu, a semi-nomadic group which were living in Canaan or nearby, and whose God he calls YHW, a clear cognate of the YHWH of the Old Testament. The question, of course, is whether these semi-nomads in Canaan, with a god called YHW can be identified with the Jews. The answer is that it is quite likely that they are one and the same. If true, this is a very exciting find, as it does a couple of things to support the Old Testament.
First of all, it will push the earliest evidence for a Jewish nation all the way back to the time of Moses. That is awesome for Christians. Second, it will show that the Jews were as a monotheistic or at least nearly monotheistic people all the way back to the time of Moses. Third, it will show that the name of the Jews’ God was YHWH, beginning at least as early as the Old Testament itself tells us that this name was used of the God of the Jews. So many skeptical criticisms of unbelievers would be settled by this discovery, if we can conclude that it is indeed a reference to the Jewish people and their one God. It has them showing up in Canaan at the right time and with the right name for their God. It also supports the conservative biblical timeline for the Exodus–one that I have always ascribed to, but which some liberal and even some conservative scholars have questioned recently–preferring a later, 13th century date for the Exodus. This is amazing support for the Old Testament narrative!
Of course, a responsible Christian will remain just a bit cautious and not declare the question solved once-and-for-all. However, as believers, we are not at all surprised at this discovery, as every time a new and bona fide archaeological discovery is made which is relevant to biblical historical statements, they always, without exception, support the reliability of the Bible. No surprise here, as I have always believed that the Bible is inspired by God and that, therefore, it is the most reliable source of historical information we have for the ancient Near East.
You ask when I think that the Exodus happened. I have always believed, based on the biblical accounts, both from the Old (Exodus 12:40) and the New (Paul, Galatians 3:17) Testaments, that the Exodus happened somewhere around 1430 BC, and the partial conquering of the Promised Land happened somewhere around 1390 BC. The Soleb Inscription lends much credence to this biblical timeline. Let the naysayers take note.
Are the Shashu of the Soleb Inscription the Hebrews of the Books of Exodus, Numbers and Joshua? Probably so, as so much of the data lines up (time, location, name of YHWH), but we should remain at least a bit cautious about declaring this a fact. Why does Amenhotep III call these people the Shashu–a name not found in the Bible? This question needs to be resolved. Does this support the historical narrative of the Old Testament? Seemingly yes, and to a really great degree!