According to the wikipedia page, Cox’s theorem first appeared in R. T. Cox, “Probability, Frequency, and Reasonable Expectation,” Am. Jour. Phys., 14, 1–13, (1946). Prior to that, I don’t think probability had much in the way of philosophical foundations, although they may’ve gotten the technical side right. And correct use of probability for more complex things, like causal models, didn’t come until much later. (And Popper was dealing with the case of science-in-general, which requires those sorts of advanced tools.)
According to the wikipedia page, Cox’s theorem first appeared in R. T. Cox, “Probability, Frequency, and Reasonable Expectation,” Am. Jour. Phys., 14, 1–13, (1946). Prior to that, I don’t think probability had much in the way of philosophical foundations, although they may’ve gotten the technical side right. And correct use of probability for more complex things, like causal models, didn’t come until much later. (And Popper was dealing with the case of science-in-general, which requires those sorts of advanced tools.)