TBH it all depends on how you define an "IC CPU". The MP944 needed several support chips to actually be a computer, but then so did the 4004 and the Four Phase Systems AL1. I can recommend a good video by Alexander the OK on youtube (https://youtu.be/YpruA5mC7wg) that goes into a lot of detail about the MP944 and its contemporaries (which I feel like OP has watched too)
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[ 1.2 ms ] story [ 16.0 ms ] thread> The first microprocessor existing on a single chip was the contemporary Intel 4004.
CPUs made from multiple chips had been around already, I believe.