The history of FIR filters
Let me propose a majorizing date for this discovery, at least in written form: Rader, C. M. and Gold, B. (1967) Digital filter design techniques in the frequency domain, Proceedings of the IEEE. Such a discussion appears on page 164, under the name of "frequency sampling filters", involving the combination of "elemental" and "comb filter". They say "The phase versus frequency is exactly linear except for discontinuities of $\pi$ radians. These discontinuities occur where the magnitude response is zero".

A lower bound could be Lerner, R. M. (1964) Band-pass filters with linear phase, Proceedings of the IEEE, which seems to keep analog.