In many ways the ENIAC was more like an FPGA than a computer. It was programmed with patch cables connecting the different computational units as well as switches, and had no CPU as such. The cables had to be physically rerouted when changing to a new program, which took weeks. My understanding is that it was eventually programmed to emulate a von Neuman machine around 1948/49. As far as I understand, this was done mainly by Jean Bartik based on Von Neumans ideas.

If this is correct, it was not a von Neuman machine originally, but it eventually became one, and at approximately the same time as the Manchester Baby.