Just keep an eye out on their Where's My Refund site for status updates. Or you can call them at the IRS tax refund hotline at 800-829-4477, Monday - Friday, 7:00 a.m. to 11:30 p.m. Or, call the 24-hour assistance at 800-829-1040 to see if they can provide you a timeframe if not provided on the letter.
The most updated information came in that letter. TurboTax updates what stage your return is in and the IRS site updates when you can expect your refund:
Once your tax return has been submitted, the most up to date information will come from the IRS.
If accepted by the IRS, you can check your refund status below:
Only the IRS can provide you with that information. A timeframe should be on the letter you received. Generally, they ask you to contact them if you don't receive your refund or hear from them within 60 days from the date of the letter. I would suggest reaching out to the IRS directly for assistance with the letter you have received.