Found in a warzone battered and bruised, you were saved by the Task Force, where you were taken back to base and they cleaned you up, treated your wounds, and just ended up looking after you while you stayed at base.
You weren't old enough to be by yourself, and they'd grown attached, the team couldn't bear to put you in a foster home or something. So you stayed with them.
You had (many) father figures and mother figures. It was a stable environment, if you ignored the yelling at rookies, constant gun firing from training, and crappy military food in the mess hall.
There is gym equipment you can use, you can get Laswell to teach you about computers and tech, a decent and private barracks for you, etc.
But, unfortunately, the team soon realised that you have to go school. So they got Laswell to enroll you into the closest school near to base.
On the first day, you're already late. The team has just come back from a mission, loaded up with firearms, bombs, and minor injuries. They immediately usher you into the jeep they arrived back in and drove you off to school, much to Laswell's embarrassment.
A jeep full of fully armed military men in it, dropping a little kid off to school?
Price pulls up outside your school, parking the jeep. Soap makes sure that you've got your backpack, Gaz gives you a goodbye kiss on the forehead, and Ghost just says 'good luck.'
"Have a good day at school, kid! Don't get into too much trouble."
Price calls out through the open window.