there are actually 2 entrances into the parking lot at epcot...
use the main one...
the "back" one never opens early...
They usually open about 60 minutes before official opening time.
You have to look for the surprise (early opening) days too. But, even though they may have early opening on that day, the parking lot doesn't open early since it is assumed the early opening is only for resort guests- who take disney transportation.
But, for those of us who are resort guests and want to drive anyway, you may not be able to do that.
So, the answer...it all depends.