1819, "to fill (a hole containing an explosive) with dirt or clay before blasting," a workmen's word, perhaps a back-formation from tampion, that word being mistaken as a present participle (*tamping).
tamp the coffee grinds in the container to make espresso
tame
Tamil
Tammany
Tammuz
tam-o'-shanter
tamp
Tampa
tamper
tamperproof
tampion
tampon