I read all the class descriptions.
Reading and comprehending nuance are different things.
Explain how a fighter gets proficincy with every weapon and armor in the game but others don't?
How does a wizard learn wizardry and multiple spell slots.
Where does a rogue's expertises come from?
Sure, a fighter gets proficiency with every weapon and armor in the game because he's a special person and his mother was a special person and as a child taught him everything he needed to learn the basics of every weapon. He has a natural talent with weapons that Bob the militia man does not.
The wizard learned all those spells because she was bit by a magic spider that gave her dreams and understanding.
The rogue has expertise because her father was 1/4 kinder!
Do you get it yet? The 5E rules don't say how a starting character got it's abilities. Maybe training, maybe a blessing by a god, maybe from years of experience, maybe anything. It's up to each player to decide how/why their character is special/knows what it knows.
D&D used to have class based age modifiers in 3e to explain the time that training for a class takes. 5e has a few limited methods of gaining profiecincies as training and it takes time.
You said it yourself, "used to". 5E doesn't have any of that, therefore it's not applicable to 5E RAW. 5E doesn't say anywhere that gaining proficiencies at level 1 takes any time at all. You keep melding things from past editions into the 5th edition. That's fine at your table, but that is not RAW or RAI.
There is a training time, either alone or via an instructor.
Wrong. In 5E for level 1 abilities there is no such thing. Prove me wrong with a quote from an official 5E source, not what the 3E or 2E, or some 3PP product says. You won't find it in 5E.
But if commoners, bandits, goblins, and kobolds could pick up a longsword and instantly be a fighter, D&D 5e would not the the easy mode people claim it is.
PCs are special. They are the rare, the unusual. It's why NPCs are not built (RAW) with PC classes. It's why sidekicks don't have abilities comparable to PCs at the same level.