Of course it's entirely possible, depending upon your use-cases. If you want to use your phone as a communication, navigation and browsing device then there is no need to touch Google. You can disable Play, Maps, Chrome, Drive etc and install alternatives. Even WhatsApp offer a direct APK download, I wish more vendors did.

But if you want to play the latest games , install your bank's app or use voice agent then you'll need Google Play and an account.