Most guys who shoot big bulls do it because they have been hunting elk a long time and know what to do for the opportunities on the big bulls. Very few really big bulls are killed by chance, though it does happen, even on public land.
In my book any elk is a trophy. You usually have to work hard for them, get into their territory, make a good shot with a bow or a rifle, then get several hundred pounds of animal to your truck, camp, and to the cooler eventually...
Since this would be your first hunt, set your sights a lot lower and enjoy the experience and learn a few things about elk hunting. After a few trips you may get lucky or learn enough to find a big bull and have a tag in your pocket at the same time... I've seen very big bulls on public land that I'm pretty sure would go around 400, but always had a spike tag or cow tag in my pocket, so had to just watch them walk away... my son and I saw a huge bull elk a couple years ago while deer hunting. We were driving to an area to hunt after our morning hunt and a huge bull walked across a meadow about 50-60 yards from us like he owned the place. If there was a 400+ bull elk in that unit (and there are) this was one... he must have known it was deer season and he was also in the rut because he was in no hurry to prance across that meadow. It took me an awful lot of years hunting in some very rough country to get my first decent 6 x 6 elk and I think he would score around 300, but I've never measured him.... I was more than tickled to get him and relive the hunt every time I see him on the wall...
