Taking a book from Mario Golf Super Rush, where speed golf is after making a shot, you have to rush to your ball placement.
Take that into Minigolf where now you have to explore the map on foot and have all holes active at once and see who can finish all 18 holes the fastest.
Being able to explore the maps on foot would be tricky due to how some of them are laid out. There’s the large gap over the body of water in Forest, Dark is mostly void once you leave the bit that’s decorated near the holes, Kingdom has sections that are inaccessible on foot unless you also had access to movement items (same with Altitude), the cave section of Alpine could be weird to get in/out of, hole 18 of Treasure Cove is, iirc, quite a ways away from the cave you see at the end of hole 17.
A race mode mutator has been suggested in the past (1, 2), and I think a first-in-the-hole mutator is already planned based on this message from Mac saying how it’s maybe one of his favorite of the upcoming mutators.
I like the idea of the all holes active at once part, being able to asynchronously go through the levels regardless of the pace of the other players seems like it’d be neat, and is something I think I’d like just in regular golf too.
I would think the world would be modified to accept the changes to "speed golf rules to allow to get in and out of places that are far apart or underground
Island or Waterhole would be a good start to start the new mode in as the map can see all holes at once.