Given the snowpack this year and the most recent storms (last week into next week) would the end of June still be good for climbing via Avalanche Gulch?
Thanks.

Most definitely yes. I am not sure where the snowline will be... but you'd be looking to have good coverage from at least Helen Lake and up. This will certainly be the case and likely for a good bit below that as well.

I wouldn't be surprised if it was in decent shape into August.

For a first time climber, would the last week of May be better than the first week of July?
Thanks.

Picking a date with stellar weather is probably more important than the time of year. I’ve found terrible weather in June and I’ve had perfect weather in February.

Most likely, we'll give it a shot during the first week of July. Hopefully, we get some good conditions then.
Generally, at peak snow level (like right now), is the climb steeper? But, I believe, it might get a bit more windy late into the season (July) with increased rock fall risks..?

Avalanche Gulch is a good route--there may be some rocks coming down--especially late in the day. I'd try to Summit before noon for sure.
Clear Creek on the other hand is good year round if you don't mind scree and a short scramble section. I've done Clear Creek in late Fall and it was good.
Avalanche Gulch is probs fine--the sooner the better just due to rocks mostly.
have phun!

Avalanche Gulch will be packed the first week of July due to the holiday... biggest risk is probably being hit by falling climbers.

Very encouraging!
Hopefully, I'm not one of those "falling" climbers. This would be my first time with crampons and iceaxes..
Do people attempt without crampons? I mean, with Crampons, what are the chances of a slip?
thanks!