Difficult to say, unfortunately. For starters, the website actually says "the week of the 19th," so in theory it could be anytime next week.
Additionally, this is the first time in recent history that Texas has used a standard Round method of applications instead of their previous rolling application method. That being said, there isn't any information from previous years to go on since there weren't any deadline dates previously, as far as I know.
Here's hoping they start on friday for a great start to the weekend!