Our goalkeeper restarts before anyone is ready

I would keep the instinct to restart quickly, but add one check before the ball goes. “Is somebody ready for it?” That is enough for U10. You can recreate the moment in training by starting lots of games from the goalkeeper and rewarding the team for recognising when the quick restart is actually available. Sometimes the best decision is immediate. Sometimes the keeper needs two seconds so teammates can turn, move or spread. I would not replace initiative with a slow routine where everybody has to reach a marked position first. Quick and rushed are different. Quick means the player has seen an advantage and used it early. Rushed means the player has acted before the picture is there. Help the goalkeeper learn that difference.