Why didn't I get a possible deposit date for my tax refund check

[paynesweetness]

No direct deposit date from irs After refund was accepted by the irs

[CatinaT1]

Once your return is filed, TurboTax has no control over the processing of your return or the release of your refund. You will need to continue to watch the IRS Where's My Refund site for a date to show.

Due to PATH Act, the IRS holds refunds for EITC/ACTC customers until March 3.  

Here are a couple FAQs to track your refund:
When will I get my federal tax refund?
How do I track my state refund?
Why does Where's My Refund say "approved" but TurboTax still says "accepted"?

Why do some refunds take longer than others?

What if my IRS refund is taking longer than 21 days?

[DoninGA]

The IRS does not give a possible deposit date on the IRS website until the federal tax refund has been issued.

After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions