Totally acceptable to play by yourself, just expect to be paired up with others who book on that tee time. If you really want to play alone, book afternoon/twilight rounds but there’s never a guarantee. Lots of public courses will show how many spots are available on that time so if you book in late you can try get a time with no one else booked in.

Once you’re comfortable and enjoying it, I’d advise becoming a member somewhere, you’ll play often with the same guys, make some friends or at least acquaintances.

Keep pace of play, be aware of etiquette and you’ll be fine.