Say I agree with your distinction - or restriction. There was still software written for, and programmed into, general-purpose, Turing-complete calculating machines long before there are CPUs.

So let's look at the technical details of the word. The term "Software" was coined in 1958 by John Tukey. The computers in use at that time were machines like the IBM 704, the PDP-1, and the UNIVAC 1107; these are all vacuum tube computers that contained no silicon microchips and no CPUs. Even technically, the term "software" predates silicon and CPUs.

Non-technically, I disagree with your premise on the basis that it's often been argued - and I agree with the argument - that humans are just computers with software personalities programmed by social conditioning, running on wetware and a fair bit of firmware. And there's increasing evidence that there's no real CPU, just a bunch of cooperating microorganisms and an id that retroactively convinces itself that it's making the decisions. Even if the term "software" wasn't coined until 1958, software has been a thing since complex organisms capable of learning from experience arose.

Unless we're all living in a simulation, in which case, who knows if software or hardware really exist up there, or whether there's even a distinction.