Odds of Getting In
Becoming an archivist is a mixed bag. First, there's obviously the secondary and postsecondary degrees you'll need, which will take time and push your career's start date into your late twenties (at the earliest). Then, there's actually getting the job, and there's more competition than you might imagine.
And even after you get that job, you realize it's a short-term grant-funded position, so you have to prove that you're still needed after the job has been completed or else you're back out there on the street with a "Will Organize 4 Food" sign.
Your first year or two may be a struggle, but it's not a totally hopeless cause. There are loads of places to work as an archivist, from museums to newsrooms to corporate headquarters. This diversifies what and where you can archive at the beginning of your career. You can also do a bit of freelance work, helping individuals put their family histories together. Keep pushing, and eventually someone will pay you to get their stuff together.