Federal income tax, while extant in some ways prior, was broadly established in 1913 with the 16th amendment[1].

Other than very high war profiteering tax rates imposed during WWII - which were not only refundable but also removed over time - there is almost no connection at all between WWII and the broad concept of federal income tax.

[1] https://en.wikipedia.org/wiki/Sixteenth_Amendment_to_the_Uni...