At that instant, it exploded with a tremendous noise.

Literal

That instant, big-sound [together with-とともに] exploded.

A compact dramatic moment. ~とともに ('along with,' 'together with,' 'at the same time as') is a formal/written connector used to mark simultaneous or accompanying events. 大音響 ('great noise,' 'tremendous sound') is a register-marked compound — 大 + 音響 (sound effect, acoustic) — giving the event a deliberately loud, cinematic quality. The missing subject of 爆発した is recoverable from context (the thing that exploded). The word order — time expression first, then the event — is typical of narrative climax: setting the moment before delivering the action.