This worked for me (without creating google account).
1) Create new User Profile (call it 'Telegram' or whatever) and then in the new profile:
2) Install google play and dependencies from GrapheneOS Apps icon.
3) Download Telegram api from their website and install.
4) When running through the Telegram setup menu it often crashes - but restart and allowed any permissions it asks for (network, phone, notifications). Importantly, there was one last permission that flashes before crashing (for me anyway) - then never shows again - it just keeps crashing. It is CALL LOGS. So go into the apps, permissions (for Telegram), and allow call logs.
5) At some point you will be sent an sms. If it doesn't come through it's probably been sent to your default profile (it was for me). So, staying logged into Telegram (in the Telegram User Profile) log back in to your default profile, get the sms code, go back into the new profile, and start the Telegram setup menu again - it should allow you to enter the code and complete the setup.
6) Stay logged in to Telegram in your new Telegram User Profile but switch to your default User Profile.
7) Install Telegram api from their website (perhaps the F-Droid one would work too - and might be better as it will update) in your default User Profile.
8) After entering your phone number it will 'send a code to your other device'. Switch to your new Telegram User Profile and you should have a notification from Telegram with your new code.
9) Go back into your default User Profile. Go back to the Telegram setup wizard, enter the code, and you should be in!
Note - this will not work if you are trying to restore an existing profile (as it will send a code to the other device that you don't have access) to. I've lost my old account and had to create a new one. To do this I had to change my existing phone number before starting the process above.
Anyway, very relieved I don't have to create a Google Account! Good luck!