I remember an architect saying:

The bridge is 20% a bridge and 80% how to put it there.

There are several ways, but can be grouped in:

Remove the water, literally temporarily reroute the river.

Redirect the water: build a dam around the future pillar location, drain the spot.

The floor is lava: rework the ground on the two sides to make it firm enough to place massive equipment, from which you launch the premade bridge over the gap.

The floor is lava but old school: you build a lightweight wooden/whatever bridge from the shore into the river, join with the same structure coming from the other side. Use this structure as a platform on which you build the bridge.

The pointy stick: you stick giant sticks in the water and put the bridge over those sticks.

The suspended thing: you build a cablecar-like thing, from which you deploy wire after wire until you have a “golden gate”thing. Then from those wires you work your way down to build the road part.

Ice is your friend: stick pipes in the water, run coolant in the pipes and create an ice wall. It can be done to help in any of the above methods, where applicable. Even to freeze the terrain to prevent water to filter into a hole/excavation/whatever.

In all cases, the problem is not being under water, most construction hate water or hate being jointed in water. So even if you are the chief of the scuba planet with millions of scuba soldiers, you probably want the structure to be built in a dry environment. Then you can flood part of it, but only after it’s assembled or cured.

The above methods can be mixed in many ways.