In the PDF of your TurboTax return, the last page of the federal return should be an "electronic postmark" that shows your name, Social Security number, the date and time that you e-filed the return, and the date that the IRS accepted it.
There will be a date and time stamp for when it was received and accepted.I think there is also a Show Efile History button in the bottom left corner.
When you efile you get back 2 emails.The first email only confirms the transmission.The second email says if the IRS (or state) Accepted or Rejected your efile.