1945, from Mexican Spanish, from past participle of Spanish tostar "to toast" (see toast (v.1)).
Entries linking to tostada
toast v.1
"to brown with heat," late 14c., from Old French toster "to toast, to grill, roast, burn" (12c.), from Vulgar Latin *tostare (source of Italian tostare, Spanish tostar), frequentative of Latin torrere (past participle tostus) "to parch," from PIE root *ters- "to dry." Related: Toasted; toasting.