Well, you're right - a really good high school program starts at the elementary level, but it doesn't have to. A high school squad could slowly be built over a few years without having a youth program (though the skill level may not be as high).
But to answer your question, all you really need is a volunteer willing to run the program. I suppose this person would collaborate with whoever runs the youth football. I'm sure there will be no problem finding a TON of little girls lining up for skirts and poms. And there are probably lots of parents who would love to coach, but maybe didn't know how to start it up or thought that since a program didn't exist that it couldn't exist.
Since you are coaching one of the football teams, you're in a great position to start (or help start) organizing the initial stages of a cheerleading program. Once there's some kind of outline/idea of structure, find someone willing to make it happen.

Hi,
Thank you for your time and answer Chelsea. It was very informative. I think this is a matter that needs to be addressed at the next bossters meeting. Hopefully this is something that we can get off the ground. Again, thank you for your reply.

-Coach Jay

You need to find an experience coach that is willing to do a full time job for part time pay. There are plenty of girls who want to be a cheerleader but without proper instruction and leadership the program with not thrive.

Figure out what the booster club is willing to do and offer to restart a cheer program. Then find a coach that fits your needs.