I have a SFF pc with an AMD GPU and AMD CPU both with better specs that the new Steam Machine just waiting for them to release a standalone installer for SteamOS :(
I just use vanilla debian and Steam works great. Just set it to launch steam on login and set your system to auto-login, that should get you most of the way.
Have you tried Bazzite? It’s basically a drop-in replacement. It’s based on Fedora’s Atomic stuff instead of Arch, but if it wasn’t for the logo at the start, I’d be hard pressed to notice I was using it and not vanilla SteamOS.
I did try using Bazzite but I had weird issues with stuttering/throttling on the RX 7600 which made most games totally unplayable (I confirmed the same hardware worked fine on a windows install). That was a while ago though, it's probably worth me trying again.
Normally I just use regular Fedora/Arch/OpenSUSE for gaming on Linux and never see any issues (albeit that's on a 6800xt at the moment) but I want that consolized experience.