Unitedstatesofamerica1 ball looks to be about 1 inch to 1.5 inches - to me. No size are given. I have found none in that size which I think are native American made.
You say: So pecked is, without question, man made?
Note that all are man made. Clay marbles made by early historic settlers and native American are man made, just at a different period in time.
Early historic tend not to be pecked. They are made through a different process than native american.