I'm not sure I'll be able to come up with a reason for the crew to NOT just drop him off at the next space station. If the character becomes a burden to the rest of the crew they will totally do that to be rid of him.
Why is this not true for all the rest of the characters? Being dumped by the crew if they become a burden, that is.
That said, I think theres always a problem when one person misses the start-up session, and then want to make a character that kind of deviates from the norm. For me, I would put a much bigger demand on that person to adher to what ever was decided in that meeting rather than their own preferences (withing reason). Cause I've experienced the situation several times (both as a GM and as a player) where this happens, where the starter group had a great plan on how the group should work and what kind of game it would be, and then the late commer came in and kind of ruined it (I have seen it work too, by the way. So I'm not saying it's always bad).
That said, I think a kid is a very fitting and clasical role in a group of space truckers. First of all, no one needs to be the kids parent. If you wan't a family connection, I'd suggest something a bit more distant like an Aunt/Uncle or an older cousin or something like that. That removes a good bit of the responsability from the older character, and also changes the power dynamic a bit so the older character don't have as much authority over the younger character ("You're not my dad!").
That also means that it's perfectly viable for the older character (although the player should agree to this) not to actually want the kid there! The kid just showed up with a letter from the older characters sister, or brother or something saying "my situation is all messed upp right now, I need you to take care of the kid for a few months". Heck, that setup would even work with a character as one of the parents. Just take a look at Real Steal of to incorporate a youngster to an unvilling parent =D
But depending on the exact setup you're going with, if the kid is a bit older (and remember that age is relative! Even a 20-year old could be a "kid", if they are inexperienced and all the rest are a bit older. It doesn't feel weird when Han Solo calles Luke "kid", does it?) and the truckers are actually working for a company, the kid might have gotten a job by lying about their age, and now is part of the crew. Or maybe there's a specific task on the ship that requires a kid (someone smaller, presumably) like cleaning the airducts, or maybe a hard to reach place in the engine that needs constant attention.
You ask each character why their specific character _needs_ the kid to be onboard. For one, it might be because they are the current care taker. For another, it might be because they need help with the engine. A third might just like the kid and want to make sure they are brought up right. And if most of the characters really want the kid there, it's okay for one or two characters to not want it (as long as it's the characters that don't want it, while the players are cool with the setup). But I think the majority of the characters should want the kid there, to make things run smoothly.
Also... I've not read the acutal rules yet, I'm just talking from a fluff perspective here. But I assume the rules have some pros and cons regarding being a kid. I'd stick with those, and be carefull to apply a whole lot of additional "cultural" cons to it. Unless it's purely "comsmetic", like:
"Hey, no kids in here! This is a bar!"
"The kids with me!"
"Oh, well okay just keep an eye on them then."
Otherwise, it can easily feel like the player is being punished for wanting to play a kid. And it might also spill over so that the other players start to feel overly burdened by having a kid along. work together to make it work instead.
But I actually think you should have another "session zero" in this case, and discuss how you can make this work in the group. And if the rest of the players don't like, maybe the one wanting to play a kid needs to accept that latecomers sometimes need to adapt to the situation?