I’ve heard Maths Olympiad is very competitive and most of the people who get into camp/team are either geniuses or have been training from a very young age.
What are the prospects of someone starting late like me to excel?
If you are referring to NZ, then the short answer to your question is no - you don’t have to be a genius.
Firstly, the NZ camp selection is incredibly flawed and speaking from personal experience, there were a large group of people who got into camp that couldn’t really do maths. This is because they get their tutors to do the selection problems for them, and then submit those as their own work. There’s no test or background checks at all to weed these people out (whereas for Chem Olympiad camp you have a selection test as well as multiple assignments.)
I personally only started Maths Olympiad a few months before camp problems were released, and managed to complete them myself, eventually getting into camp in Year 11/12. I did feel however that I started a little bit too late, especially at camp where some people had been doing the same stuff for years and had significantly more experience.
I’d say Maths Olympiad is not all about intelligence or “being a genius” but rather about how much time you are willing to commit to it. You really need to learn how to solve the problems and you’ll soon see similar methods that keep coming up over and over. From my experience, this makes it largely a game where the top performing students aren’t necessarily the smartest, but rather those that have dedicated the most time. This obviously means the earlier you start the better, but by no means is it ever too late to start if you are committed and passionate enough to put in the hard yards.
I’d also recommend getting John Jiang - one of the top tutors at Crimson - who works with practically every. single. member. of the NZ IMO team (and most of those candidates who get into camp). He can teach you some of the methods and give you resources that largely cut down the time you need to spend on this, especially if you feel like you are starting a bit late. He really helped me get up to speed and he’s easily the best tutor I’ve ever had - he actually makes Olympiad Maths look easy 
Hope this helps - feel free to reach out if you need any clarifications.
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I second this. Maths Olympiad needs to revise their selection procedures.