Sounds like you need to put in for Wyoming antelope. That’s so long to wait for an antelope tag.Archery deer (most units) and archery fall turkey are over the counter tags. Some bear tags are over the counter.
That is about it. Everything else is a draw, and some are tough. Took me 18 years to draw my last elk tag. 25 years with still no AZ antelope tag.
Deer draws can be every year, or 20+ depending on unit and season choice. Elk are the same.