Traditionally, historians place him around 1250 BC, under pharaoh Ra-Moses II ("given birth by Ra"). Their arguments are very weak.
If you use the Bible dates, Moses lived around 1480 BC, 480 years before Solomon started building his temple. Although 480 can be symbolical (12x40), I believe that 1480 is approximately the date of the Exodus, with a margin of 20 years.
My interpretation, based on Egyptian and biblical history:
- until 1484: Thot-Moses II ("given birth by Thot") convicts his adopted son Moses to death for killing an Egyptian. Moses flees to the Sinai, were he marries Sippora. The Hebrew slaves are building the cities Luxor and Karnak (Ex.11.1), with the temples of Amon-Ra.
- 1484: Thot-Moses II dies. His wife Hachepsut becomes the unofficial pharaoh, because her nephew Thot-Moses III is still a child. Moses returns to Egypt and Hachepsut gives her adopted son permission to leave Egypt with his people.
- 1468: Thot-Moses III is old enough to take the throne. He sends his army after the Hebrews and removes the name Hachepsut from the official history writing.