Is the buoyant force on an object is the reaction force?

Suppose you have a weightless box that is 1cm square.

Suppose you push it down into some water, to a depth of 1cm.

Since you are displacing 1 cc of water, the weight of the water you are displacing is 1 gm.

So you are pushing down on the water with a force of 1 gm (I know that's mass, but bear with me).

The water is pushing up against you with a force of 1 gm. That's the reaction force against your push. That's also the bouyancy force.