But if the brickwork requires cleaning down and most will, then immediately after building and when the mortar is ”touch” dry,brush or sponging can commence.
If the mortar is not “touch” dry on the surface, you will need to be careful not to drag mortar out of the joint back onto the face of the bricks as you clean down.
For cleaning, use a bucket with roller and a board with foam rubber sponge. Press the sponge across the roller, this way the sponge is only moist, not over wetting the brickwork or mortar.