You´re born with your personality. If it's just genetics or sheer luck (! :happy

doesn't really matter. The point is that you´re born with it.
Most of the connections in your brain are formed before you´re born. That there isn't a lot of information in there yet has nothing to do with the cognitive functions, since those are mostly based on the wiring.
The question that always follows this is: "How do you know that cognitive functions depend mostly on wiring?"
The answer is pretty simple. Nobody experiences drastic personality type changes. (mentally healthy people of course.) This means that information does not change the processing preferences of your brain. Using the word brain here is important as well. The preferences for using one cognitive function before another is not your personal preference. If you´re an INTJ or INFJ for example, you do not choose to use Ni as your first funtion, you do not have that choice. Not even your brain makes this choice as it can not even do so. Your brain isn't conscious, it does not have a sense of self, it does not have needs. Only you do. Your brain is just a machine and simply wired for it. This is also why brain damage (mental illness) can be used as a reason to be found not quilty in court as it wasn't the owner of the brain that made the choices.
Political preferences for example can and do change. You´re not born with a political preference and your political preference may change drastically many times. This means it's based on information, it's not wired into your brain.