If you didn't mail with any method that has a tracking option such as priority mail or certified return receipt, then you'll just have to wait and see.  I like to use return receipt just for such peace of mind.

If you are a due a Federal refund, then it can take up to 4 weeks for a mailed return to appear in the IRS "Where's My Refund" tool.

If you had Federal tax owed, and enclosed a check, you should know when the check is cashed.

Your TurboTax page will continue to say "ready to mail", since it will never know if you actually printed and mailed it or not.  TurboTax does not mail it for you.