Asunto (Spanish for “subject,” in the sense of, “theme”) come from the Latin for the same, assumptus (“taken”) — from which we get the almost identical English, assume.
Interestingly, assumption originally had a fully religious connotation, something we often forget or I sometimes vaguely remember today: you’re received into heaven. An assumption, in its modern sense, is really just a religious belief actually!
The Latin root assumptus itself comes from ad- (“up, to”) and sumere (“to take”) — so when you assume, you’re really “taking it up”!
The a‑s-t of asunto maps clearly to the a‑ss-(m)-t of assumption.