I've been wondering just how mandatory id.me is. Out of curiosity I tried to find if there was a way to address the problem you mentioned without using id.me. Buried very deeply in the Q & A via a link called "alternative options" it says

If you can’t verify your identity online, you can call the telephone number on the letter you received from the IRS telling you that you may be eligible to receive advance Child Tax Credit payments (Letter 6416)

But... the link to Letter 6416 goes to a PDF that has no phone numbers on it at all.

So although id.me might not be strictly speaking mandatory, in this case it seems impossible to avoid, since the "alternative option" isn't really there.

It's a Kafkaesque nightmare.