The water would need to displace the air inside the sub and the air doesn’t have anywhere to go.
Push an upside down glass into a sink full of water. The water can’t fill the glass because it can’t move the air. Or, put your finger over the end of a straw and put in a glass of liquid. No water goes into the straw until you move your finger.
If the pressure in the air is higher then in the water it will not flow up into the submarine. Most submarines do not have a moon pool except in movies. Some have regular pools though. The closest you get on a regular submarine is the trash shoot which contains an upper and lower hatch, only one can be opened at a time to prevent the water from flooding the submarine. It is theoretically possible to increase the pressure inside the submarine a bit, maybe twice the pressure, and then open both hatches at periscope depth to form a moon pool from the trash shoot. But it is more likely to send special operatives through the torpedo tubes as they are bigger.
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