How can I proceed with filing for my taxes and hearing back from the irs about approving it so I can receive my stimulus payment?

What tax year are you asking about filing?  You cannot file a 2020 return yet.  The IRS will not begin to accept 2020 returns until late January.  You have to wait for all of your income and tax documents for 2020 to arrive--which happens in January/early February--in order to prepare your 2020 return.

If you mean your 2019 return  -- did you start preparing it but it is not yet filed:

Online tax preparation and e-filing for 2019 returns is now permanently closed.  You had until midnight on Thursday, October 15, 2020 to finish and attempt to e-file; if your e-file was rejected you had until October 31, 2020 to make corrections and re-file. Now it is too late to use online software or to e-file. If you have any changes/corrections at all to make to your 2019 return, you now have to complete it using desktop software, which you must download to a full PC or Mac  (not to a mobile device).Then you need to print, sign and mail it.

https://ttlc.intuit.com/questions/2559403-how-do-i-finish-a-prior-year-return-that-i-started-in-turbotax-online

If you already paid for your online software you can ask customer support for a download of the desktop software.

They are available from 5 a.m. to 5 p.m. Pacific time Monday-Friday.

https://ttlc.intuit.com/questions/1899263-what-is-the-turbotax-phone-number

If you are getting a refund, there is no penalty for filing late.  If you owe tax due, then file and pay the amount due as shown on the Form 1040, but expect a bill later from the IRS for the penalty and interest you will owe.  Only the IRS will calculate this—TurboTax will not calculate it.