The first episode of Crisis on Infinite Earths confirmed that Tyler Hoechlin's Superman has already faced Doomsday. Hoechlin's version of the Man of Steel has won viewers over on Supergirl, to the extent that The CW has now signed off on a spinoff starring Hoechlin's Superman and Elizabeth Tulloch as Lois Lane.
Supergirl season 5, episode 9 sees the return of Superman and Lois Lane in the first part of Crisis on Infinite Earths. The Arrowverse has been building up to this crossover for a long time, and naturally all attention is focused on who will live and who will die, and on the ultimate fate of the DC Multiverse. But the episode also contains an interesting, intimate scene that confirmed the Arrowverse's Superman has already faced his greatest challenge.
When the episode opens, Superman and Lois are living on Argo City, and Lois is mocking Kal-El for the fact he's struggling to put a diaper on his newborn son, Jonathan Kent. She teases him by listing his greatest achievements as though she were writing a newspaper piece, and notably describes Superman as the man "who's faced off Doomsday." It's an exciting reference, because it confirms that this monstrous creature already exists in this reality, and is part of Superman's personal history.
The villain Doomsday is best known for his role in 1993's "The Death of Superman" event. He's an almost unstoppable force of sheer destruction, and revels in chaos and bloodshed. Even the most powerful members of the Justice League were tossed aside by Doomsday, defeated with horrific ease, and ultimately only Superman was left to stand in the creature's way. The battle moved across the United States, and in the end the two fought one another to a standstill outside the Daily Planet. In the end, each struck a fatal blow, and both died. Of course, these are comic books, so the death didn't exactly last; still, it's remembered as one of the most iconic stories in comic book history, and defines the '90s attitude towards violence and death-and-resurrection arcs.
It seems that Tyler Hoechlin's Superman has indeed faced the Doomsday of his reality. This is just a throwaway reference, of course, so it's impossible to say whether or not this Doomsday was as powerful as his comic book equivalent; or even whether Superman died in battle against Doomsday here, only to come back from the dead. But it would certainly be fascinating to see Doomsday return in the Superman series - presuming Earth-38 is somehow restored now the Crisis has destroyed it.