So if everything is chosen at Level One and progresses without change all the way to Level Twenty, the subclasses are actually just classes. That's hilarious! 5e has had to invent more than a hundred classes!
Technically some subclasses are gained at 2nd or 3rd level. Specifically, it’s 1st level for Clerics, Sorcerers, and Warlocks, 2nd level for Druids and Wizards, and 3rd level for Barbarians, Bards, Fighters, Monks, Rangers, and Rogues. But in my experience, players generally decide at character creation what subclass they plan to take when they reach the appropriate level.
I also can’t stress enough how much they aren’t classes. Your class determines your starting hit points, hit points gained at level up, weapon, armor, and saving throw proficiencies, some of your skill and tool proficiencies (with some coming from race and background as well), some of your starting equipment (with the rest coming from your background) or starting gold, what levels you get ability score increases (or feats) at*, your spell list, spellcasting ability, and any specific spellcasting rules of you’re a caster, and class features at most levels.
From your subclass, you get about 4-6 features, spread out across as many levels.
*almost every class defaults to getting these at 4th, 8th, 12th, 16th, and 19th level, but Fighter and Rogue both grant additional ones at a few levels.
Classless systems are a thing. I don’t think that would be the right choice for D&D. But I do think 6e should change the relationship between class and subclass. I would much rather class give those fundamental structural things, while more specific features came from subclass, and characters could be further differentiated based on which subclass features they chose at levels where they gain them. You see the
hint of this kind of relationship in a few places, like the Battlemaster subclass for Fighter, and the Warlock class in general. But for the most part 5e squanders its own design space.