I agree that is is strange format, but one that the author wants for a book. Variants of this is often seen for hymns in the Swedish hymn bok, where there are no bar lines, but music “as normal”.
Yes, one could make it C,0.5 and X on 2nd note, but that would add a bar line between 1st and 2nd note, and even if I remove the bar line in Illustrator, the spacing will not be correct as the barline reserves space left and right.
I would suggest simply adding the “time signature” (it’s not really a time signature, of course) as a text item, making room for it using the note spacing tool in Engrave mode.
OK, open-time and then insert C as text object? Is there some ‘guides’ (guide values) so that I get a consistent distance compared to “real music” samples made by Dorico’s functions, or does it need to be “by eye”.
There are no specific features in Dorico for faking time signatures and producing identical spacing, no. If you want a real time signature with the proper spacing, you should, you know, use a real time signature.
Or in this case enter with Insert Mode a quaver rest, use c,39 as time signiture, then hide the rest and fix the spacing in Engrave Mode. You might need to use force duration on the Breve at the end.