There were a number of chaotic periods in Egyptian history, known as “Intermediate Periods.” Exodus took place either during the second or third “intermediate period.” Probably during the 3rd, which was c. 1150 BC. Most Eqyptian histories note that the New Kingdom was already in decline, exhausted by constant warfare in its Asian possessions. Egypt’s control over Palestine and Syria was lessening, and local tribes were assuming autonomy. Due to chaos and internal instability, there are few surviving records from this time. That the Israelites would take advantage of the situation to make a “prison break” to Canaan is not surprising. Nor is it surprising that there is no Egyptian record of it.
This is well after the eruption of Thera, but coincides with massive volcanic eruptions elsewhere.
Egyptian “Intermediate Periods”. I am of the opinion that exodus occurred after the Second IP. The Hyksos conquerers of that period were also known as the “Shepard Kings” and were probably nomadic invaders from either the Middle East or the Western Desert or both. During that period the Isrealites may have been relatively autonomous. Once the Egyptians became ascendent in the 1500s BC they might have clamped down on the shepard peoples including Israelites to the point that it became intolerable.
After the 90 year reign of Tutmoses III, Amenhotep II had to deal with uprisings of the tributory states in the Middle East. This went on for some time and would have added to animosity toward Middle Easterners (Isrealites) settled in Egypt. In 1500 BC plus or minus 50 years there was a major eruption of Etna, and I think that it might have had an impact on the Nile watershed leading to the various plagues. I think that as this was a major volcanic event, there may have been other volcanic action, such as on the Arabian peninsula, i.e., “a pillar of fire by night, and of smoke by day”.
A smart guy like Moses, who might have been a ward of Queen Hatshepsut who was co-ruler during the last days of the ancient king Tutmoses III might have been involved in various palace coups and disturbances leading to his exile in the desert and later the decision to lead the Israelites out of Egypt. There was a major effort to wipe the Queen’s existance from the Egyptian royal record. So I am putting the Exodus in the 1400’s BC. Naturally the Egyptians would leave no record of such an embarrassing event. That’s my theory, and I’m sticking to it.