I think this is incorrect, this isn't the first trained multi-layer neural network.
Minsky & Rosenblatt's https://en.wikipedia.org/wiki/Perceptrons_(book) covers multi-layer neural nets.
Rosenblatt's electronic implementation, the Mark I https://apps.dtic.mil/dtic/tr/fulltext/u2/236965.pdf
Minsky's electronic implementation, SNAC https://en.wikipedia.org/wiki/Stochastic_neural_analog_reinf...