After you file

You can print this page and click on efile history at the bottom of eac return   https://turbotax.intuit.com/tax-tools/efile-status-lookup/

And in the program check here, don't know if you can print this
In the Desktop program open your return and go up to menu item
File > Electronic Filing > Check Electronic Filing Status

You don't have to print the full return.  Look through the pdf file for the Postmark Report showing the date/time the tax return was e-filed and the date it was accepted by the IRS.