Mummification went back into Egyptian pre-history. Started with burying bodies in hot dry desert sands, which preserves them. Then elaborated progressively from there (something similar happened in other places, like Peru). They did not believe in reincarnation, but certainly saw the afterlife as involving a material body (later burials included a shabti - a ritual doll - with the inscription 'when in the afterlife I am called to work in the fields, you, my shabti, will go and work for me'). They don't seem to have taken this to a literal extreme - after all mummification involves removing the brain and internal organs, which would make it hard to function as one does in this life.