You are, of course, assuming that we don't have a soul OR you're assuming that our souls are limited to our physical brains.There's strong evidence of that. Sensory perception, memory, emotion, personality, and thought are all functions of the brain.
When you die, your brain decomposes and those things (you) are gone.
...unless you can evidence a mechanism by which they are saved. Can you?
As of yet, science is unable to answer the question: Do we have a soul?
So anyone claiming we don't is either ignorant or lying.