As far as I know - and we still had some tube radios at home when I grew up - they were used pretty much right away. For radios, and replacing mechanical relay switches, over which there obvious advantage was that since the tubes were not mechanical they would last longer, especially important in systems with lots of them.
So I'm not completely sure and somebody with definite knowledge should chime in, but I think they were not some "we have no idea what to do with this" but where useful from early on, as soon as the manufacturing method was solid. They were used for "normal" electronics well before they were used for the early computers. Even though Google search - which I just tried - also seems to have a bias and mostly associate those vacuum tubes with computers and forget all about the many other uses. It was the predecessor of diodes and transistors in addition to being better than mechanical relays.
https://www.engineering.com/story/vacuum-tubes-the-world-bef...
https://www.nps.gov/features/safr/feat0001/virtualships/vrmo...
(just one of the earliest commercial use cases as example for how short the period was between invention and wide-spread use)
> Dr. Lee deForest invented the vacuum tube in 1906. His tube, which he called the "audion," was first developed as a detector of radio waves and was quickly adopted by shipboard operators. Later experimentation, by deForest and others, showed the ability of the vacuum tube to generate radio signals with far greater precision than earlier systems. By 1914 the essentials of tube-based transmitters had been worked out.