Yes you wait until July 1st if you didn't put in for the draw and not draw out.
Good luck with public land access. There's a reason there's lots of leftover tags in certain units. It's mostly private land and pay to play. It can be done, but you might face a lot of competition. I learned this the hard way a few years ago myself as I'm fairly new to the game too. It can be done, but you have a lot of research ahead of you.