Snow in Sierra’s for July 2nd start

July 2 start from where? Campo? KMS? Somewhere else?

I wouldn't anticipate too many problems in the Sierra at that time. There still be some snow hanging around on north faces of passes, and some areas where snow hangs on later into the year, but I'd expect the trail tread itself to be largely snow free and/or packed down.

NOBO? That is pretty late and you won't have much at all. SOBO, you might get some in the North Cascades but not much there either.

https://www.postholer.com/snow/Pacific-Crest-Trail

Currently sobo in sierras on average it is between shin to hip deep. At trail heads under 7000 it is clear but there are still periodic spots. Even when it's only a couple inches deep it is slick and crunchy from daytime sunshine. I would assume by July is they don't have anymore snow storms it will be clear.