I'd be out there end of June!
Even if the elk will change their patterns closer to season, you can still learn the terrain, find new or old sign, water, glassing points, etc. It'll help you better develop your game plan for the year and then you can fine tine it on your next scouting trip or when you go out to hunt.
In NM they usually draw end of April.... I start my scouting in my and then go all the way up until my hunt.
My first set of cameras goes out beginning of June then end of June do some boots on the grounds scouting and then if I can squeeze in one at end of July I will
I do a lot of scouting during my hunt and determine a game plan then as I always find new pockets to explore. Then I get some cameras out in May or June, boots on the ground by the end of the month.
In July, I will most likely take the family camping where I am going to hunt for the final scouting trip.