Use the following TurboTax website for an e-filed tax return that will show the date/time the e-filed return was transmitted and the date the return was Accepted (if Accepted) by the IRS or State - https://turbotax.intuit.com/tax-tools/efile-status-lookup/
If you printed and mailed the tax return, then TurboTax has no way to know when or if the return was filed.
