Try https://gitlab.com/api/v4/users?username=??? where ??? is your username. This will only work if you are already logged into gitlab.
Alternatively, go to https://gitlab.com/profile/account and copy your Private token. Then run the following command from a bash-like terminal:
curl --header “PRIVATE-TOKEN: AAAA” https://gitlab.com/api/v4/users?username=BBBB
where AAAA is your private token and BBBB is your username.
Thank you a lot!
It will be nice to see this instruction be added to FAQ.