You have to be more specific with the timeline. Transistors were invented in 1925 but received little interests due to many technical problems. It took three decades of research before the first commercial transistors were produced by Texas Instruments in 1954.

Gordon Moore formulated his eponymous law in 1965, while he was director of R&D at Fairchild Semiconductor, a company whose entire business consisted in the manufacture of transistors and integrated circuits. By that time, tens of thousands transistor-based computers were in active commercial use.