Update: I spent half a day on this and I have confirmed that I can create a user customized, branded URL that will link to a users profile page.
This requires:
1) Capturing a deep link to a users public profile page
Can be done with some a undesirable and hacky UI:
Deep linking to a row must be done with a list and they can only be captured by a user triggered action that writes the value to a column. So you need to direct the user to their public profile in a list and have them click a button to generate and save the link. 
There is some quirkiness that I am working through now. I don’t have any experience designing an app that supports both anonymous & signed in users so I am plodding through it.
2) Creating a UI to enable a user to select a unique keyword so they can claim domain.com/keyword
Can be done with some clever google sheets scripting and glide logic. Haven’t prototyped it but I am confident that I can make it work.
3) Creating a custom redirect URL from domain.com/keyword to their profile page’s deep link
I prototyped this with integromat + rebrandly
4) The deep link is immutable
I have no idea if this is the case!