Definitely "to dig"
bore, break up, bulldoze, burrow, cat, channel, clean, concave, deepen, delve into, depress, discover, dredge, drill, drive, elevate, enter, excavate, exhume, fork, go into, gouge, grub, harvest, hoe, hollow out, investigate, mine, penetrate, pierce, pit, plunge, probe, produce, quarry, root, root out, rout, sap, scoop, scoop out, search, shovel, sift, spade, till, tunnel, turn over, uncover, undermine, unearth
Just use a thesaurus and you can find synonyms, but none of the words are as general as to dig! You cannot say: The child or dog or mole is excavating/bulldozing/excavating/unearthing/etc.
To dig is the best translation.