Yes, possibly the help desk can confirm receipt with the submission ID https://www.irs.gov/e-file-providers/e-help-desk-for-tax-professionals

Thanks @George4Tacks .  The number worked.  I called three times, and each time I was told the estimated wait time would be 15 to 30 minutes.  For the first two times, I waited hours until like 5 pm and got transferred to a message that says the office hour was over. 

The wait time for the third call was actually 17 minutes.  In case anyone calls, the first info I had to provide was my EFIN number, then my firm info.  After all that it was the client's info and the date it was accepted.  In my client's case, the efile was accepted.  I was directed to call another number to find out the processing status.

Anyway, George, check out the expanded services under Option (6) and (7) below, the IRS may be able to help you, too.

Phone Options has changed. Please listen to all the menu options before selection. Use the following bulleted options as reference.

From the Main Menu

• Press (1) for e-File, ERO, ITIN related information
• Prese (2) for e-Services related information

From the (e-File, ERO, ITIN) Sub-Menu

• Press (1) for Individual Returns
• Press (2) for Business and Non-profit returns
• Press (3) for e-File Application
• Press (4) for Suitability
• Press (5) for Acceptance Agent Application
• Press (6) for hearing problems 
• Press (7) for problems with excess gas