Computer Engineer here.
It depends on how much you are willing to go deeper.
If you buy a Z80 you cleary haven't designed your CPU.
If you make a CPU using integrated circuit (like 74181), have you designed a CPU?
If you use just IC like nand have you designed a CPU?
Or maybe the TRUE CPU it's that you have to place CMOS?
The image that I have attached it's the Intel 4004 schematic, and that it's one of the simplest great CPUs you can find.
Today if you design a new CPU it's not that you start by placing CMOS one by one, it's more a high level proces,the same way as you use libraries in programming.
So to answer your question it depends on the abstraction level you choose to rely on and you current understanding of digital electronic.
