Units resolve instantly correct? So can you still react to Brynhir?

Yes, you're right — units resolve instantly when finalized (Rule 337.1.c). So no, you cannot react to Brynhir herself entering the battlefield. There's no window between her being finalized and her being on the board.

However, you can react to her "When you play me" triggered ability, which is a separate chain item. After Brynhir lands, that trigger goes on the chain as a Pending item, and both players get a Reaction window before it resolves (FEPR process). If you have a Reaction-speed response (like killing her or bouncing her), you play it here. Once the trigger resolves, opponents can't play cards for the rest of the turn — even if Brynhir has been removed in the meantime.