1922, "to use an escalator," back-formation from escalator, replacing earlier verb escalade (1801), from the noun escalade. Escalate came into general use with a figurative sense of "raise" from 1959 (intrans.), originally in reference to scenarios for possible nuclear war. Related: Escalated; escalating. Transitive figurative sense is by 1962.
The Allies escalated the bombing
*es-
Esalen
Esau
escadrille
escalade
escalate
escalation
escalator
escalatory
escallop
escapable