It seems most likely that Joseph rose to power during the time of the Hyksos, or just before in the 12th Dynasty when many Asiatics came into Egypt. It also seems most likely that the Exodus from Egypt should be equated with the expulsion of the Hyksos.
"It seems most likely" is NOT evidence.  Do you have any physical EVIDENCE, as in Ancient Egyptian writings that a massive Hebrew Exodus took place?

Did you read my Article?  Where are the Archeological remains of a 40 Year Sojourn in the Desert?  Not one bone, (human or animal), or pot, or artifact, has been found from 1.5 million people and their animals, living there for 40 years!  How do you sustain such a large population and their livestock in a barren desert for 40 years? 

Where are the Stone Tablets of Moses?  Where is the Golden Ark of the Covenant?  How come there are no signs of them anywhere?  There is not one shred of hard evidence which proves the story.