Odds of Getting In
The best way to increase your chances of becoming a certified, bona fide, fireside investigator is to spend some time on the back of a fire truck. A lot of time, actually; just like the best detectives usually start as uniformed crime fighters, so too do the best fire detectives start as uniformed firefighters. Many training programs prefer you have a strong base of firefighting to go along with your fire science knowledge (source).
The good news is, fire departments actually want solid and capable fire investigators (go figure), so they're more than happy to offer advancement to any firefighter willing to step up to the next level. They may even help you get your certifications if you've been dedicating your life to keeping your community flame-free.