Using the fretting hand thumb to mute or manipulate lower strings is something experienced guitarists do after years of practice.

The best place for the thumb is comfortably behind the neck and your index/middle finger, but not firmly. Try re-watching Guitar Fundamentals 1, how to hold a guitar by Lisa McCormick, for a precise guide. Or how to fret notes, the video on what the job of the fretting hand does.

Best of luck, Chris.