No----that is normal especially now. Mailed returns take much longer, especially during the current pandemic.
It can take 3-4 weeks for anything to show up on the IRS site when you mail a tax return. Expect 6-8 weeks for complete processing of a mailed return.
If you mail a tax return (or a payment) to the IRS, it is a good idea to use a mailing service that will track it like UPS or certified mail so you will know it was received.
When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s.
TurboTax will not know anything about your mailed return, and will continue to show “Ready to Mail” on your account. TurboTax will not know that you put your tax return in an envelope and took it to a mailbox. TurboTax does not get updates on mailed (or e-filed) returns.
When the IRS opens its mail and begins to process mailed returns you can check the status on the IRS site. https://www.irs.gov/refunds
State returns have to be mailed to the state.