For trophies, AZ and NM are king. Not that big goats can't come from a lot of western states, but a lot less frequently.
My last AZ pronghorn tag (my ONLY AZ pronghorn tag) was a 27 year wait as a resident This year. But I definitely made good on it.
NM has landowner tags, and most guide services will have availability. Drawing a tag is highly unlikely in your first 10+ Years as a non-res. We have gone the last 6 years in a row on landowner tags. And no, there are no extras on the ranch we hunt. Same guys get them every year.
WY is a good option. Tags can be drawn after a few years. Some of rhe better units with more public lands might take 5-8 years to draw. Last winter was brutal on the pronghorn population in the western portion of the state.
MT has some places you can buy a tag over the counter, on some Reservations. Goats are not big, but they are there.