1620s, "to fall, drop, or stomp (on something soft) with crushing force," possibly imitative of sound made in the process. The figurative sense of "suppress completely" is first recorded 1864. Related: Squelched; squelching.
squelch any sign of dissent
squeal
squeamish
squeegee
squeezable
squeeze
squelch
squib
squid
squiggle
squinch
squint