Do you consider software in a computer to be mechanical? You could record the 1010101 in an electricity stream and conclude there is no meaning to that electricity beyond getting from point A to point B in a chip.
/s
If we're looking for something supernatural like a soul, then we shouldn't expect to see natural evidence. Thus the lack of that evidence does not imply its nonexistence. Relevant xkcd: https://www.xkcd.com/638/
Sure you can say that our lack of evidence means nothing since we don't have the capability, through natural laws, to acquire that evidence.
But that's just another way of justifying faith as a rational argument.
The only reason we have to believe in the supernatural is mythology. And the only reason we have to believe mythology is faith (and fear).
There isn't any evidence that there is anything happening that's not biological despite 1000's of years of searching for that evidence.
And there is all kinds of evidence that biological processes can explain our experience. More all the time.
It's not definitive in the sense that we're anywhere near completely understanding our biology.
But it's the most likely explanation, given what we do know, but such a huge margin that there is no real alternative explanation outside of mythology.