When will taxes that were e-filed start being accepted?

Even though it's possible to efile now, the IRS hasn't  opened up return processing yet this year. The IRS doesn't open up to start processing returns until January 27. If you efile before then, your return will just sit on TurboTax servers until the IRS retrieves it on Jan. 27 (except for a few returns that are pulled early for testing purposes.)

So people should start hearing something soon after January 27 (unless it's pulled early), but there may be a backlog at the IRS at first.

Your return is still in pending on the server because the IRS will not begin to accept/reject/process returns until January 27.  Only a few returns were accepted early in a test batch.  Everyone else has to wait.

https://www.irs.gov/newsroom/irs-opens-2020-filing-season-for-individual-filers-on-jan-27

So watch your emails and spam folder to make sure you know after Jan. 27 if your return was accepted or rejected.