You definitely take a squad with you on the first mission. I think this is just a casualty of streamlining the play procedures and just not updating the text. I’m pretty sure the starting procedure used to be that you chose roles at the beginning. However, I think it was changed to make it easier to get into the game. Consider:
You gather your friends together to play a game of Band of Blades. You give them the pitch, give them a quick rundown of the history of the world, the nations, the gods, chosen, the cinder king and undead. Then they choose roles and fill out those sheets, making a bunch of choice solely on the context you just gave them. Then you have to choose a Chosen, and choose their special ability. Then you give them a mission, and they each need to create another character, a specialist this time. Then the Marshal chooses a squad and assigns the specialists and you have to make rookies. At this point you’ve possibly made 3 or more characters before you’ve even started playing!
All that to say, I can see why the designers decided not to frontload everything - but I think something got missed in the shuffle. I can’t think of a good reason to not allow the squad - you want to introduce the dynamics of the game right off the bat, and a lot of the game to me is managing the squad as a resource, either using them to increase your position/effect or having to mitigate damage to them.
Just my two cents.