There is no way to do that. To whom do you need to give proof that you used TurboTax? Your receipt for your payment to TurboTax will show that you paid for the software. The emails that you received if you e-filed are also proof that you used the software.
There will a cover letter that says Turbo Tax. Download the full pdf with all the forms and worksheets.
Here's an alternate way to print by opening the filed return back up to print at the Print Center, where you can also get the worksheets.
Log in and at the Tax Home or in the section Your Tax Returns & Documents for 2020, look for a link Add a State. Click on Add a State. (you don't really add one. That's just to open your return back up.)
After the return is open, click in the left menu column on TAX TOOLS, then PRINT CENTER.
Then choose Print, save, view this year's return.
The next screen should offer some options: Just my tax returns or include government worksheets (optional), or include government and TurboTax worksheets (optional.)
But realize that Turbo Tax is a self prepared return. Only you sign it. What do you need it for? Just preparing it with Turbo Tax doesn't mean you filed it.
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.
Your return's electronic filing status history records all e-filing activity related to the return, including the Electronic Postmark. You can print it out if needed.
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp -- enter the Social Security number of the first taxpayer on the return and the ZIP code to retrieve your filing status history.
TurboTax CD/Download software
(Windows) From the TurboTax File menu, select Electronic Filing > Show Electronic Filing Status History.
(Mac) From the TurboTax File menu, select Check E-Filing Status.