It looks like you are going when the big game is out and about.
May - June (link)
Elk, moose, deer and bighorn sheep introduce their newborn calves, fawns and lambs to our Rocky Mountains.
Resources:
https://estes-park.com/explore/google-trekker-hikes
https://www.tripadvisor.com/Attractions-g60945-Activities-Estes_Park_Colorado.html