There is a desktop client for Play store called Racoon. When I used my phone for several years without a Google account, from time to time I would need some app (for taxes, bankning, public transport, whatever) that was distributed via the Play Store exclusively, but I had no problem downloading that APK using Racoon and installing it separately. You don't get notified of updates, and updating is a manual process, but for for a single user that wants to avoid the Google services it's workable.