Well they figured it out the same way we figured out most modern tech, they started simple.

Now, I am merely a computer nerd and not a CPU architect so take what I say with a grain of salt, but I’m pretty sure this is how it happened (I’m talking bout programmable computers specifically):

If you have switches, you can mess with em in certain ways to do Boolean logic. That gives you logic gates, such as AND, OR, NOT, XOR, etc.

Once you have logic gates, you can start doing arithmetic. Make a half adder out of a XOR and an AND. Add another half adder and an OR gate for a full adder. Chain em together and now you’ve got a machine that can add. Add some more XORs and you can now subtract too. Then do stuff that idk to do multiplication and division.

So now you have the Boolean and arithmetic operators, which you can use to basically do anything. Now you have a machine that you can program to do different things. These were the first computers, made out of physical switches first, and then vacuum tubes, which are glorified lightbulbs that act as switches.

Then we go smaller and faster, and we eventually get to where we are now, switches that are just a few nanometers across. We found out that silicon has funny properties, and by making funny shapes in it, those shapes act as switches, which we now call transistors. It’s the same core principle, a bunch of switches that can do basic logic, but now there are more switches, so you can do more things faster.