The PhB has rules for characters of all levels and offers that a character can start above 1st if the DM agrees, and the DMG has rules for starting at higher levels. Many posters on this board might have joined an ongoing game at 1st level where there were others at higher levels. (I remember one with a bunch of 1st levels and a pair in the double digits. And the higher level ones were good at not stealing the spotlight, but rather stopping TPKs). The DMG even has a suggestion of having lower level followers in case someone dies so a player can just grab one of them as the new character, so clearly parties of mixed levels can be a thing.
So,
@hawkeyefan,
@Vaalingrade, or anyone else who doesn't particularly like DMs to restrict things when they don't need to, if my character idea for your new game is an experienced 3rd level war-wizard, a 5th level former mercenary captain, or an exiled 9th level monk... are those all good to go in whatever game you're running? If not, why not?
It depends on the situation. I'd talk to the group about it and see how they wanted to proceed. Then we'd likely do that. If for some reason I didn't think it could work, I'd likely point that out. But if everyone else was convinced, then I'd probably give it a shot. If I felt very strongly that it wouldn't work, then I might say "I don't think I'd like to run this" but I doubt it would get to that point.
But beyond that general approach, I generally begin a game with PCs at level 1. We use milestone leveling, and we don't punish new PCs or anything like that, so the groups in my game very rarely have any disparity in level. I don't think such disparity is generally a good idea, although I think 5e is pretty forgivable in this regard. But the larger the gap, then the more this will impact play, and I expect be dissatisfying for at least some players. So most of the time, all our PCs are the same level.
One exception to this is a longstanding campaign that dates back to our earliest days as a group; there are two groups of PCs, one from 5e and one that has been converted from our earliest days playing AD&D. The converted characters are level 17 and the 5e PCs are level 14. But each player has one of each, and they tend to split into groups along level lines (though this is less true as that gap has lessened).
Another example that I shared earlier in the thread, for one campaign, our group collectively designed multiple PCs to populate the starting area. A couple of the PCs began at Level 2, representing a bit more experience that they had, but in each case, they had much more responsibility to deal with. The one level increase in ability seemed like a reasonable tradeoff for the fact that those characters had more specific roles to follow. But even then, we all picked out of a hat, and the remaining PCs became NPCs that could serve as replacement PCs if needed. So no one made their decision based on level.
Aside from those kind of rare exceptions, though, I don't know if I hold Starting Level as the same kind of option as character race or class. Generally, level is something you obtain, not something you select, right? Also, it's a game element, generally separate of the fiction except in the broadest way, right? If someone had the idea of an experienced character.... like an old veteran who's been a soldier forever...then we'd likely come up with a way to represent that, but I think character level would be one of the last options I'd consider.
So it all depends. There are multiple ways to handle it, and multiple reasons for any given approach. And again, I'd like to repeat, I'm not against limits or restrictions. I'm against....for me, and as general advice to anyone else....the default approach being "the GM decides all this stuff."