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According to https://en.wiktionary.org/wiki/machina#Declension the case of "machina" only can be nominative, vocative or ablative.

As the meaning of the phrase is "god descended on the stage by means of a machine", obviously isn't vocative and I find the ablative possible... even reasonable.

Maybe interesting link: https://www.reddit.com/r/latin/comments/366c46/deus_ex_machina_is_this_god_from_the_machine_or/

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    Well, you could easily eliminate the "wrong" cases. 1. It can't be nom, (it's a dependent word, "deus" is the head, i.e. the most important word in the phrase; 2. It can't be voc. either (you are not addressing the machine, "O dear Machine! Hear me out"). 3. So it must be abl. and this is confirmed by the preposition ex, which is used with abl. en.wiktionary.org/wiki/ex#Preposition – Alex B. Sep 11 at 17:42
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The case here is ablative. The preposition “ex” preceding the word “machina” is one of the many common usages of the ablative case.

This could be the ablative of place (from), or as you can in your English translation, ablative of means.

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