No. Current User is a state that represents the user agent. It’s read-only.
Of course you can get some other User object and operate on it, but that object is not “Current User” (unless of course it happens to be the same as Current User).
Current User is a metaphor for “who is viewing this page?” or, more precisely, “what agent is accessing this page and what is it’s authorization state (logged in vs logged out)?”.
Note that this is not the same as “setting Current User” (which we can’t do) but Current User takes on the identity of the authorized User. This is the same as accessing your Bubble app’s API or the equivalent of “run as…”
You actually have the password. Not sure how you would set the password though, you have to know it through that user interacting with it i think. If you don’t know their current password you can’t change their password either. So I may as well put login screens in, it’s not as hard as all that, just thought there might be a workaround.