According to Genesis 10, the Philistines were descendants of the Casluhites (Ge 10:14) and Caphorites (1Chr 1:12), who lived in Egypt before migrating to Canaan. So the Philistines of the time of Abraham (c. 2000 BC) were probably Egyptian in origin, explaining why we find no evidence of Aegean peoples that far back. The Aegean Philistines came later, either conquered or intermixed with the original Philistines, and then built their Pentapolis.
If you want a source for this, this article covers it in mild detail. I don’t agree with everything, but they make my point that there is no contradiction.
That, or you have your chronology mixed up. Unless the Bible is completely erroneous on its chronology, the Exodus could not have occurred any more recently than perhaps 1450 or 1500 BC (dates I personal disagree with, but I digress). If the Exodus occurred in 1130 BC, then King Saul and Moses must have been contemporaries, since Saul became King c. 1100, about a decade before Moses dies in your chronological framework.
The average lifespan for Abraham’s family at the time was about 170 years. Sarah, at 68, would have been about middle-aged, and would go on to live for another 59 years. And depending on how well you age, women can still be beautiful at 60 and 70 today.