Mobile app is currently working to access for me (desktop is not)... but still doesn't show Soarin' availability (at last for 6/4), and never did (even at 7am.)
Also, Tier 1 for Epcot on 6/4 is still:
Illum
Living with the land
Mission Space
Soarin'
Test Track
Yes I remember having the same issue when I was booking a Soarin' FP for the June 17 opening. Soarin' appeared on the site but said there were no Fastpass+ times available. Once they really opened up later that day I had no issue getting the time I wanted.
Soarin' FPs are showing up on the date I am looking at now (6/28) when before it was saying none available. Perhaps things are slowly being sorted out.
This was the same thing that happened when Fast Passes were released for the new Soarin. Lots of waiting and waiting and website not working until later that day.