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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/
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.
