I'm able to start surfing on still water (Terrain tag 6), unless I'm facing up.
The red arrows are the side I can't surf onto the water from. Any other side works fine.
I've looked at the example maps, and I still can't figure out why I can't surf on this map, but I can in the examples. I'm using the same tileset as the example maps. To be specific, I'm using Route 2 as comparison.
In layer 3 there is an invisible tile over those tiles (scroll up just a bit in the tileset and you'll see one labelled "Free pass"). This overrides the passability of that clifftop tile, and allows the player to surf north off it or walk north onto a bridge from it.