They had trouble with simultaneous releases when they put out 4e, there were some troublesome proofreading/quality issues. So with 5e, they put out the pieces one at a time, allowing each title to have its own turn to be the urgent, top priority.
I started running 5e before the release of the Monster Manual 5e, using the smattering of monsters in the back of the PH. It was limiting, but fun in its way.
In an OSR game, you only fight when you have to, because victory is not a foregone conclusion.
You might also "roll up" your character instead of creating one. Which everyone should at some point, because it's a whole part of the game that's disappeared. If you hate trying to come up with a character concept, you might well love a game where the dice can give you some ideas.
Most modern OSR games will tell you that characters have no "plot armor" and are just as vulnerable as NPC's, just like they were in the old days. But read the rules, and the PC's actually do have some plot armor after all, just a bit less.