What payment are you trying to prove? To whom? Your only proof that you paid your federal or state tax due will be your own bank or credit card record.
Did you e-file? Did you click a big orange button that said “Transmit my returns now?”
When you e-file your federal return you will receive two emails from TurboTax. The first one will say that your return was submitted. The second email will tell you if your federal return was accepted or rejected. If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.