Right now, video thumbnails will always start at full volume (and will not consider the video settings linked to your logged-in YouTube account either). This is not very user-friendly as you can imagine because it disrespects the volume preferences of the user.
I suggest that the videos are muted by default and that the user manually has to turn up the volume. This way, videos will not unexpectedly disturb the users, nor disturb them when they have specific volume settings that causes these video thumbnails to be very loud.
This is very similar to Steam store pages, where videos are also muted by default.
(edit: took out example I provided, because it’s no longer accessible. The gist of the example was: RIP my ears.)