We can't give you an exact date at this time. Refunds can be issued in less than 21 days, but there are cases where it can take longer to process.
TurboTax will only show the status of returns (not refunds), such as when the return is actually accepted. You would not be able to directly track the status of your refund from within your TurboTax account. TurboTax is not connected the IRS or state department(s) of revenue refund tracking tools.
Please see the TurboTax FAQ below for more information on tracking your tax refund:
https://www.irs.gov/refunds
The below information explains the process of what happens after you send your tax return for approval:
https://turbotax.intuit.com/tax-tips/tax-refund/wheres-my-tax-refund-the-irs-refund-timetable-explained/L9ZoW82cT