Is this usage pattern not common in your English? It's quite common in mine and is accepted by pretty much everyone without batting an eye, except, maybe, only maybe, some English instructors.

Where are you from?

It works as stands if "the missing continent" is a singular concept (which is the premise of the story, that this undiscovered continent was believed to exist).

Compare "The tenth planet hasn't been found yet" vs "The planet that hasn't been found yet". If "the missing continent" was used then, like "the tenth planet" is used now, it works.

I think this...

"The missing continent. It took 375 years to find."

The "that" puts the emphasis on the continent, as if it was it's fault that it took so long.

While we're at it, let's ditch the Eurocentrism and make that "... that took Europeans 375 years to find again"