Origin not responding

Does EA have any support forums? If so, check there to see if any other users with Apple Silicon are having any issues (or even if Intel Macs are having issues). Is Origin even compatible with an Apple Silicon Mac?

You are connected to the Internet when you are trying to log in? If you are using any VPN, or proxies, then they may be interfering or blocking your connection to EA servers.

Are you running any anti-virus apps, cleaning/optimizer apps, or third party security software? If so, then they may be interfering here. Uninstall those apps by following the developer's instructions since those types of apps are not needed on a Mac and usually causes more problems than they solve.

You can try booting into Safe Mode to see if that makes a difference in case a third party app is interfering, but it is also possible that Origin may not work in Safe Mode since Origin may need to install some of itself in the lower levels of macOS which will be disabled while booted into Safe Mode.

Otherwise @stumpy1946 is absolutely correct, that EA will need to assist you.

Origin is not an Apple product. If you're having problems using it, you need to contact Origin tech support for help.

If they tell you it's an Apple problem, remind them they are responsible for making their product work with Apple's OS; not the other way around.

3rd part developers being of no help is not that uncommon to me. Still, it's their product; not Apple's