Any time you like
Some ambiguously defined flood happened, and then God cleaned up in some narratively convenient way. So, scientists can discover it whenever suits the story, or never at all.
Note: I wrote up a ton of examples, but many of them ended up being about various types of extinctions, mummies, post-flood disasters, etc.. Kinda morbid, so a lot got deleted. I figure that, if it's to be a story about God from the Bible, it should probably be more up-lifting.
Example: Scientists never discover the truth
God cleaned up everything and fixed all evidence. Even if time travel is later invented, God will redirect time travelers to a fake timeline in which the flood never happened.
So, scientists never discover Noah's flood.
Example: Scientists discover instantly
God directed the waters to etch the message
God was here.
in the side of every mountain, in divinely beautiful writing. Intense lightning bolts struck these locations so powerfully that they altered the stone itself, causing it to glow in a beautiful display.
Beneath each signature, God has written descriptions of precisely what happened in every major language mankind will use for the next 10,000 years, ensuring that everyone in the world is crystal-clear on every detail.
Example: Upon alien contact
At the time of the flood, some aliens were orbiting the Earth. They actually went down and surfed some of the waves!
Whenever you like, the aliens came down to tell humans what happened. They recorded the whole thing in perfect detail across the entire world in their awesome 3D-recording technology, but they only tell humans whatever's narratively convenient for the humans to know.
Since aliens can come down and show humans what happened at any point in history, you can pick when it happens.
Example: Never, because Earth blew up
God thought that it'd be funny to remove the flood waters with a second, identical flood – only this time the water was anti-matter.
Example: Whenever they examine the salt layer
The flood waters mixed with the ocean, allowing much of the salt to rise above land. When God removed the flood waters, the salt remained, coming down like a rain all across the Earth.
Depending on how you pick the details of what happened, this can have different sorts of effects that can lead to discovery at different times.
Or, you could have God put the salt back into the oceans, restoring their prior salinity and avoiding a salt layer on Earth, if that's better for the story.
Example: Whenever scientists explain the platypus
Biologists are stumped; it seems that the platypus doesn't exist in the fossil record before the flood!
Turns out these cute little creatures very closely resemble a duck/beaver hybrid:
Upon exploring their genetic history, it looks like they were sudden created around the time of the God.
Behind the scenes, it turns out that God thought it'd be funny to create a new, cute-looking animal when teleporting the animals back after the flood, hence platypi!
The divine spark of their recent emergence helps to explain why some platypi secretly have human-like intelligence, as behavioral scientists discover whenever.
Maybe the scientist who discovers the truth is themself a platypus?