How to accept Apple Music Family invite without iOS/macOS?
No - you'll want to find a spare iOS device for your father's account to log in and accept the invitation. (or backup / wipe / set up your device for him - then wipe / restore your backup so that you don't mix streams of data signing out and then signing in as his account).

This would clearly be a bug and something you might be able to call Apple Support to see if they can push an alternate way to authenticate your father to the group.

My guess is the account is either blocked and needs apple push notification to tie it to a physical device one time and then it will work from windows. I've done this a handful of times for people that primarily are on Windows without needing to engage official support.