When an opponent goes down hurt, the first hand reaching out should be yours.

Competition has an outer edge and someone getting hurt is where it sits. For those few seconds the sides stop existing, because what is on the ground is a person who was fine a minute ago and is now scared. Reaching out first is not softness or a gesture for the crowd. It is the simplest available acknowledgement that the game was always the smaller thing.

Go over. You do not need to say anything useful, and being there is the whole message. Ask afterwards how they are, through whoever you know on their side.