Unicode \epsilon\_y

Currently, as of Unicode 12.1, there are only 40 possible subscript characters. You can see the always current list here:

All Subscript Characters

And, it appears that Julia supports most of them (I think maybe only the ARABIC SUBSCRIPT ALEF:

"   ٖ "

is missing).

You might could get away with using \epsilon\_gamma as it looks similar to “y”.

As far as why more subscript characters don’t exist, I would say it is the design goal of Unicode. According to the official Unicode Standard:

the Unicode Standard does not encode idiosyncratic, personal, novel,
or private-use characters, nor does it encode logos or graphics.

and:

The Unicode Standard does not attempt to encode features such as language, font, size,
positioning, glyphs, and so forth.