Every user should, for security and
legal reasons, have their own credentials JSONs inside their own home-dir. Locked down, so you can't enter another user's home.
Other than that, I'm pretty sure you can put gam anywhere, as long as it and any scripts you want are in all users' path.
/usr/local/bin or /opt/gam or whatever, as long as you put that in their path. It's just like any other binary/script.
But, you may probably ned a real VM, like a Compute Engine, and have users SSH in (either via web-ssh or real ssh).
I wouldn't recommend just a normal cloudshell, even if you can share access.