Matt - the CTF trekking program usually hikes the Georgia Pass segment in mid June. They are scheduled on the 17th this year. That is about the earliest it is clear enough to do it in an average year. At that time, hikers still typically encounter snow on the west side of the pass but it is passable. This year is a little drier than normal and if that trend holds you may be able to move the start forward a bit. I would guess that the second week in June might be ok for segment 6. Everything east of Kenosha Pass will probably be passable by June 1st. Segment 4 goes up to about 11,000 feet for a while and usually has snow until mid May. Segment 5 is lower should be no problem if you make it through 4. Last year the first successful hikers through segment 6 made it the first week of July, but there was more snow than this year.
Springtime usually makes the snow rotten and unstable with a breakable crust over sugary snow that won’t support weight. Snowshoes can help, but in rotten snow you can still posthole using them. Typically you will go a few hundred feet through snow then hit dry land for a few hundred, then more snow, etc. You spend a lot of time taking the snowshoes off and putting them back on. I generally prefer to just suck it up and posthole.
Waterproof boots and knee high gaiters are a necessity in the early season. Lots of extra socks. Crossing snow early in the morning is easier, as the crust freezes every night and will hold your weight better.
It is easy to get lost in the early season because the trail is not marked for snow travel. A gps is very helpful to stay on the trail.
If you are hiking the entire trail this year, you will probably have a more enjoyable experience if you schedule it so you can thru-hike it without stopping. Starting early June is probably the very earliest you could do that this year.
bearcreek