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...No. There were plenty of tests, for example the atomic pile built at the University of Chicago. They certainly didn't just do a bunch of math and then build an industrial nuclear power plant on the first go.
I don't think you're making the same criticisms they are (I last read some of those criticisms a while ago, though).
they literally did do that
the first particle accelerator was built like over a decade later
I'm not saying a particle accelerator was used to test the theoretical underpinnings of nuclear power. I'm saying testing was done, that is, they did not "accomplish[] all of that with the theoreticals." They just used earlier tools.
To test modern physics, many (not all) physicists say the tool they need is an accelerator.