Theoretical and fictional mean the same thing. A device with infinite memory is a thing of fiction, but because it's a useful concept for theories tested in math and science we label it theoretical instead.

Beyond that, the first computer was built by Babbage in the 1830s, 100 years before the Turing machine was thought up, unfortunately he died before he finished his general purpose analytical machine, but his differece engines are generally considered the first iterations of modern computers.