Straight from an adcom at UTSW:
"For example, an application submitted now would not prompt a response until August, but one submitted in June or early July might also get a response in August, since that is when we are first able to consider applications. Thereafter, it might be as early as a few weeks after submission of the application. Nonetheless, we encourage everyone to apply early (i.e. in June or July)."
Again, I'd say around late June at the latest. If you have a better GPA and MCAT score, you have a bit of leeway (not too much). But of course, the most important thing you should do right now is to get transcripts in and have LORs done ASAP. Those 2 things take the longest to do and commonly hold up applications.