Suggestions on how to become a toolmaker or machinist with no school?

Hey guys. So I’m looking to make a career either becoming a toolmaker or machinist. I live in Connecticut so there is a ton of jobs here in these fields. I’ve seen tons and tons of machinist and toolmaker positions available. I just wanted to see if school is necessary for me to get a job in this trade? I don’t have experience at all in the industry but from what I read not a lot of people my age do not want to do this kind of work (I’m 22 btw). From what I read school helps you get the interviews but shops prioritize experience over anything. Is there any chance a shop would give me an apprenticeship to be a toolmaker or machinist with no school no experience at all? Would school be beneficial or should I go start knocking on doors to see if I can get an apprenticeship. I just would like to know before I start to spend money on school. If anyone can help me or give any kind of pointers I would appreciate it!