A yes–no question that begins “Did you. . . ?” is invariably, or mandatorily, a do-auxiliary inversion. It cannot stand alone as an actual non-auxiliary. You have no verb afterwards, because to it is not English. You cannot say any of these:
- Spoke you it?
- Called you her?
- Ran you the race?
- Think you so?
- Called you?
- Gave you it?
- Proposed him to her?
- Have you it?
- Did you it?
in Contemporary English. That is super-archaic. It might not even be understood.
It is very hard, but not impossible, to make sentences with only pronouns but no verbs come off as grammatical. Here is one such example:
“What about the Smiths? I gave her a letter.”
“And I, him.”
But just having a lone, inverted do-auxiliary without a verb for it to help out on is not going to work.