Here (https://sibeliusone.com/music-for-the-theatre/einar-nilson-composer-of-the-first-jedermann-music/) is a long and interesting, IMHO, article about the composer of the first Jedermann music, written for its 1911 première and performed many times afterwards.
I was wondering how that could possibly be but I see that's specifically for Hofmannsthal's play of that name, not the medieval mystery-play... that makes more sense.
Sibelius' music for this only followed Nilson's by five years, btw.
Title duly amended to eliminate any confusion.
That said, I don't offhand know of any earlier music for the anonymous mystery-play either, though I haven't -really- looked!