For years I've used an Android phone with no Google account attached - I simply skipped the OOB assistant and then created an account pointing on my company's Exchange, where all my mail/calendaring/contacts were. For maps, I used Sygic, which you can purchase outside Play Store.

Yes, I did lose Google Play, Youtube, Hangouts, but exactly that was the intent - not using Google services. Today, it would be even easier, with the existence F-Droid providing third-party apps.