It's just barely possible it's simpler than that. First, note that the Hebrew does use a verb corresponding to sit rather than fiat:
וַיֹּאמֶר אֱלֹהִים יְהִי אוֹר וַיְהִי־אוֹר׃
wayyomer ĕlohîm: "yəhî ʾôr" wayəhî-ʾôr.
יְהִי yəhî is a 3rd m. sg. jussive of היה 'to be'.
The Septuagint turns this into the following:
καὶ εἶπεν ὁ Θεός· γενηθήτω φῶς· καὶ ἐγένετο φῶς.
γενηθήτω is the 3rd sg. aorist imperative of γίγνομαι 'to become'. Latin's 3rd person imperative is rarely used for most verbs, and gigno, the cognate of γίγνομαι, is pretty cumbersome and certainly more marked than γίγνομαι is in Greek, so fiat is a more than fair rendering of that; the Vulgate clearly closely follows the Septuagint here.
(This does mean that fiat isn't acting as the passive of facio here but just has its own meaning of 'to become' (factus est, too, is the active perfect of semi-deponent fio, not the passive of facio), but it's not clear that this is a line Jerome or any contemporary speaker of Latin would have drawn.)
So why didn't the Septuagint use a form of εἰμί 'to be'? It did! εἰμί is suppletive, with γίγνομαι supplying its aorist stem!
Was Jerome simply unaware of that? Probably not, admittedly, and he certainly did also know Hebrew and have access to the Hebrew version of Genesis, so his choice of fiat is almost certainly a conscious decision made for the reasons Joonas discussed (and the fact that he didn't use gignatur is actually a point in favour of that). But I thought it was an interesting observation.