It wasn't until the next morning that we sighted the continent.

Literal

Next-morning [becoming-になって] first-time continent [subject-が] was-visible.

~になって初めて is the 'not until' pattern, literally 'when X arrives, for the first time' — emphasizing the absence of Y up to that point. 見える ('be visible / can see') is the spontaneous-perception verb, describing what enters the visual field involuntarily — fitting for spotting land at sea, where the sighting happens to you rather than being a deliberate act.