A frame Challenge.
The theme song of the tv series Land of the Lost, 1974-1975, told how the protagonists were transported to a weird sort of pocket universe by "The Greatest Earthquake ever known".
As I remember, Geologists long ago debunked the idea of an Earthquake powerful enough to sink a continent like Atlantis. Of course what you are asking for would be the sinking of much smaller area and possibly for a much shorter distance.
So possibly we need to find out the largest area ever subsisted in any recorded earthquake, and the deepest that any recorded earthquake has ever subsisted any land.
I think that a major earthquake might drop land in an area of several hundred or thousand square miles (an area probably only tens of miles on its longest side) about a meter or so.
So maybe something else could sink sections of Panama.
I guess an asteroid impact could vaporize many mountains in Panama, instantly lowering the ground level to below sea level.
As to how that would change history, it would exterminate the human species and all other large lifeforms, a significant historical change.
It would be more plausible for a group of super advance extraterrestrials to decide they want to excavate a sea level panama canal, and make it much wider and much deeper than necessary for even the largest plausible ships to navigate through.
Possibly the aliens have records of the oceanic currents and biology from before the Panama region closed the gap between the Pacific and Atlantic oceans, and wish to recreate the species of whales and sharks (megaladons) which inhabited it.
Possibly the intent of the aliens may also be connected to the thousands or millions of cubic miles of rock their worker robots will excavate, and the islands or mountains they might build with that rock.