Hi! The temporary solution that worked for me was to login into both Steam and Amplifiers (g2g) in a another browser (safari/firefox/edge) and connect there

Edit: I did have to ensure that the cookies/cache/history on that browser were clear (or had never been used). If nothing else works, such as in @PacifistMob's case, then reaching out to one of the devs (via the discord, especially for Insiders) will alert them to the issue. 

Hey I tried again on firefox as you recommended, Steam still a no go for me for some reason (not telling me it's already synced) but amazingly epic store worked!Thanks :)
Edit: Now I've realised it's only on Steam. Urgh, I'll just wait till the game comes out

Hey I got on after some help on the discord.So in my case the trick was enabling cookies on my steam account on their website too, then it worked!
Gotta be honest I didn't even think of that but yeah enable all cookies in your Games2Gether account and Steam website account and that should fix it, hopefully.