Where can I find out the date of the day I filed?

Check Your E-File Status on this TurboTax page Filing status below:
https://turbotax.intuit.com/efile/efile_status_lookup.jsp
You will be able to see the date you transmitted your return and if it was accepted or rejected. 

Check Your E-File Status on this TurboTax page Filing status
https://turbotax.intuit.com/efile/efile_status_lookup.jsp
- It will show the date you transmitted your return and if it was accepted or rejected. 
- Both your Federal and State will be listed separately if you filed both.
- It will tell you when you E-filed
- The electronic filing date