The only way that I know of that would work is to have pre-submitted responses in the Sheet.
The Sheet would either need to be linked, so that subsequent responses get written to the correct row,
or you'd need to record the Form response ID, and match up the Form response ID on subsequent submissions.
If the Form is linked to a Sheet, then an edit (Form resubmitted) somehow automatically gets written into the previous row.
I think that the following is true, but test it for yourself it you think it might work.
If you first link the Form to the Sheet, then add a column, that added column gets skipped over when the new response is saved.
So, you can put your own values into cells in that added column.
So, the way that you would know that the Form response is matched to that persons ID, is simply that Google Forms somehow knows
what is the correct row to overwrite when the Form is resubmitted.
You don't need to prefill the user ID in the Form and then somehow get it back.
If the Sheet isn't linked to the Form and there are not original submissions, then this won't work.