I have looked at the problem that citations cannot be inserted as 1st items in footnotes once again more closely. It has become obvious for me that this is indeed a bug of org-cite or rather a default setting which was deliberately introduced, although it is not really user-friendly or practical to my mind.

I modified the function org-cite--allowed-p in oc.el and inserted 'footnote-definition' in the following lines:

;; Paragraphs and blank lines at top of document are fine.
((memq type '(nil paragraph footnote-definition)))

(I leave the comment in its original form to make the passage easier to identify.) 'footnote-definition' by the way does not appear anywhere in org-cite--allowed-p in its current form.

After this I can easily insert footnotes as 1st items in citations, and I do not get Org's warning "Cannot insert citation here".

Am Sa., 18. Sept. 2021 um 22:39 Uhr schrieb Bruce D'Arcus <bdarcus@gmail.com>:

Elias - do you mean org-cite-insert won't allow this?

[fn:1] [cite:@doe2019].

If yes, I don't see that; it inserts fine.

I'm using bibtex-actions for the insert processor, but I don't think
that should make any difference, since it's org-cite that's handling
that.

On Sat, Sep 18, 2021 at 4:23 PM Elias Bounatirou
<elias.bounatirou@gmail.com> wrote:
>
> Hi,
> When I try to insert a citation as the first item into a non-inline-definition footnote, org-ref-cite refuses to insert the citation returning in the minibuffer "Cannot insert citation here". The same problem does not occur if the footnote has an inline definition. As for non-inline-definition footnotes, if I copy the citation into the footnote, no problem occurs, either. The citation is also properly exported to LaTeX.
> Is this a problem of org-cite/org-mode in general or rather of org-ref-cite?
>
> Best regards,
> Elias