Old English steppan (Anglian), stæppan (West Saxon) "take a step," from West Germanic *stap- "tread" (source also of Old Frisian stapa, Middle Dutch, Dutch stappen, Old High German stapfon, German stapfen "step"), from PIE root *stebh- "post, stem; to support, place firmly on" (see staff (n.); source also of Old Church Slavonic stopa "step, pace," stepeni "step, degree"). The notion is perhaps "a treading firmly on; a foothold."
Transitive sense (as in step foot in) attested from 1530s. Related: Stepped; stepping. Originally strong (past tense stop, past participle bestapen); weak forms emerged 13c., universal from 16c. To step out "leave for a short time" is from 1530s; meaning "to go out in public in style" is from 1907. Step on it "hurry up" is 1923, from notion of gas pedal.
<a href="https://www.etymonline.com/word/stepping">Etymology of stepping by etymonline</a>
Harper, D. (n.d.). Etymology of stepping. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/stepping