If you mailed a paper return, then I assume you yourself physically printed, signed, dated, and mailed it. TurboTax does not mail it for you.
It can take the IRS 6 weeks or even more to process a mailed paper return.
Approximately 4 weeks after you mailed the return, it should show up in the IRS "Where's My Refund" tool, where you can monitor it here:
https://www.irs.gov/refunds
