blast (n.)
Old English blæst "blowing, breeze, puff of wind," from Proto-Germanic *bles- (cognates: Old Norse blastr, Old High German blast "a blowing, blast," German blasen, Gothic blesan "to blow"), from PIE *bhle- "to blow," probably a variant of root *bhel- (2) "to blow, inflate, swell" (see bole).

Meaning "explosion" is from 1630s; that of "noisy party, good time" is from 1953, American English slang. Sense of "strong current of air for iron-smelting" (1690s) led to blast furnace and transferred sense in full blast "the extreme" (1839). Blast was the usual word for "a smoke of tobacco" c.1600.
blast (v.)
Old English blæstan "to blow, belch forth," from the root of blast (n.). Since 16c., often "to breathe on balefully." Meaning "to blow up by explosion" is from 1758. Related: Blasted; blasting. Blast off (n.) is attested from 1950.