Great question — answering as the UphillTech team:
This is usually referred to as a J-cut . It's called this because when viewing the clips in an editing application, the audio of the incoming clip sticks out in front of the video, and makes a shape similar to the letter "J". It's also sometimes referred to as an audio lead or audio advance. Likewise, there exists an L-cut where the audio from a scene lingers after the video has switched to a new scene.
Full answer by user1118321: https://movies.stackexchange.com/a/92367 (CC BY-SA 4.0).
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