In fact, there's absolutely no on-screen evidence to support the notion that that's a universal practice, and one big piece of evidence that they don't always: the U.S.S. Enterprise-D, which was the first of the Galaxy-class ships, with the second being the Yamato.
I'm sorry? Everything I've ever seen said the Galaxy was built first, then Enterprise, then Yamato. And we've seen the Galaxy on-screen a couple of times. I've never seen any suggestion that there wasn't a U.S.S. Galaxy.