As best I can tell, this is due to a mild case of suppletion.
In Classical Greek, the verb system hadn't gotten as thoroughly regularized as it was in e.g. Latin (with its four-and-a-half nicely-delineated conjugations); different systems of the "same" verb could come from different Proto-Indo-European constructions, like with πείθω's two different aorists with slightly different meanings (ἔπιθον vs ἔπεισα). Sometimes they even came from different Proto-Indo-European roots entirely, as in ὁράω, ὄψομαι, εἶδον "to see" (from PIE *wer-, *h₃ekʷ-, and *weyd- respectively).
The present forms of βαίνω come from Proto-Indo-European *gʷem-. However, its aorist ἔβην comes instead from *gʷeh₂-. And as a result, the present acts like a thematic, but the aorist acts like an athematic. Over the millennia this irregularity, like so many others, got smoothed over, and in Modern Greek, the "aorist" form is a perfectly regular ανέβαινα.
(It's worth noting that ἀναβαίνω in particular did also have a regular thematic-style aorist ἀνέβησα, meaning "to put onto". I don't think this is attested for most other compounds of βαίνω, and isn't especially common, but does show up several times in Homer and Herodotus.)