Two Medicine - Pitamakan-Dawson

I know every year can vary, but historically, when is Pitamakan-Dawson trail clear of snow and open for hiking?

Would early July be a possible target date?

In years past, I vaguely remember the trail being closed to a grizzly bear sighting (due to possible carcass?) and the two times I visited in August, wildfire smoke made the air quality horrible...so I'm thinking of going in early July.