I worked this out for what I needed. Use the ‘?background=1’ parameter on the URL to remove all the player interface and set the video auto-playing and muted. This removed the Tap to Unmute’ on mobile for me.
<iframe src="https://player.vimeo.com/video/442480801?background=1" width="100%" height="100%" frameborder="0" allowfullscreen></iframe>