Between this from the t&cs:
Apply for or upgrade to the Venture card during the Venture Match My Miles Challenge. Upon approval, you'll receive an email with further instructions.
Register online and submit proof of your airline miles as fast as humanly possible, so you don't miss out on your share of the one billion miles. Most major domestic airline credit card rewards programs are eligible.
And the fact that no one received the emails yet,
I'm guessing that they'll FIRST ride the signup wave for all it's worth (well past 10,000 application) and THEN send out the emails.
In any case the rush is not directly how soon you apply for the card, but how quickly you reply to that email...
Just my guesses