Evidence suggests that a longer version of the saying was circulating prior to the early- to mid-19th century. The meaning is thought to come from the way clams are protected during high tide, and although the connotations have changed slightly, this original concept is still is the heart of the expression today. First Usage

This phrase is actually a part of the bigger phrase "happy as a clam in high water" or "at high tide."

Source

L. Ron Hubbard would disagree. Scientology doctrine holds that we inherit all our stress and anxiety from clams who were our ancestors, and their tension between their desire to open and close their hinge. (It is apparently possible to stress out an indoctrinated Scientologist by making opening and closing motions with one’s hand, subliminally reminding them of this.)

Clams have feelings too

https://youtu.be/IRbv518eJbs

"A task perfectly suited for a creature so limited in its doingness."