A lot vs. Alot: 9 Grammatical Pitfalls
1530s, "attack, assault," from on + set (n.); cf. to set (something) on (someone). Weaker sense of "beginning, start" first recorded 1560s. Figurative use in reference to a calamity, disease, etc. is from 1580s.
onset on·set (ŏn'sět')n. A beginning; a start, as of a cold.