The primary issue with jobs being able to start at level 1 is that they'd be forced to design and create weapons for the entire level spectrum of these jobs.

Look at GNB, for example. because it starts at level 60, it has zero weapons in the game from level 1 -59, meaning they'd have to go back and create a level 1 weapon for it to even be able to start at level 1. But then a level 1 weapon will not carry it to level 60, so they'll need to implement a ton of weapons for it. Even assuming they could re-skin or re-use every manatrigger in-game several times over to not have to design unique models for every dungeon set, they'd then have to go back and add the weapons to merchants, dungeons, etc.

TL: DR, while it's possible, there's zero chance they're doing it.