The PhB has rules for characters of all levels and offers that characters can start higher 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?