Are you sure, that the unicode letter is from the same font? Try to apply a Character Style to the very single letter and apply "None" Character Style immediately after that letter.
Another workouround could be to insert a space, but not a normal on, insert Type > Space > … and take the smallest one and try upwards to the first working combination.
I need to display the Unicode character in a separate font since it is not part of the body font.
I have now applied the None character style to it, and inserted a Hair Space afterwards as well as in front of the footnote reference. All these three characters (0x1D50A, Hair Space, footnote reference) have None character style applied to them.
The footnote reference still does not turn up (though in the footnotes, "Go to Footnote Reference" proves that the it is there, technically).
For the Unicode Character you HAVE to use a Character Style. You can apply it automatically via GREP styles. Then, you will see the footnote.