We cannot look up when you filed. We have no access to your account or your return. If you mailed your return, only you know when you took it to a mailbox. If you e-filed, look at your emails.
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.