>That cannot possibly be true. Not knowing what exactly is going on with the charge carriers at the subatomic and quantum levels is not the same as not knowing how the amplifier works

since everything that happens inside a transistor is exactly what is going on in a quantum sense, you've described "not knowing how it works". You cannot understand a bipolar transistor without quantum effects, it's the thing that creates the transistor effect.

the theory of amplifiers you go on to talk about was well developed at that time because it's the same theory for vacuum tubes.

You can empirically drive the equations that apparently govern the macroscopic behaviors, right down to details like temperature sensitivity, and the Early effect, without having a detailed model of what is going on at the atomic and subatomic level. Then what makes an amplifier work is explained by those equations. And for that not even the full detail of them is necessarily required, depending on what aspect of the amplifier we need to explain. Like basic operation versus concern for thermal runaway.

What makes the amplifier work and what makes the transistor work are separate concepts.

That's why understanding translates from tube circuits to transistors. A transistor circuit maybe an emitter follower, which has a counterpart in tube circuits known as the cathode follower. The cathode resistor creates local negative feedback similarly to an emitter resistor. Early op amps where tube circuits. They have the same differential input stage and the same basic theory of operation. You program their game the same way with resistors. The familiar Sallen-Key filter topology was first described with the help of tube circuits for reference, back in 1955. To undestand it, we don't even need the details like how amplifiers work at the component level except when we get into design parameters in which certain issues matter, like frequency-bandwidth product, or input offset current or whatever.