After we tore down an old built-in closet, this hole appeared behind everything. We have received approval from the board to seal the hole since there's quite a bit of noise coming from it. That is, cover it on our wall, not block the airflow in the actual hole

I've received great tips on the forum before so I just wanted to check how you would do it and with what material. We will be installing a new closet that will cover the hole, so it doesn't need to be super pretty, just even.