Cambridge Maths as an international student, what are my chances?

Hi, I’m a student from China in Year 13. My existing grades are A*A* in Mathematics and Further Mathematics, and predicted A*A in Physics and Economics. I also took STEP 2 and 3 in Year 12 and got double S (so STEP isn’t going to be a problem at all).
What I think might be a problem is that I don’t have IGSCE grades. My middle school used the IB curriculum, my average score was ~6 out of 7 across all my subjects, which isn’t that great, and I was told that universities may find it weird for a student to transfer two years before they apply. Moreover, I don’t have any EPQs. I did, however, start studying certain math courses that are offered in Cambridge, such as analysis and group theory (but there are no certificates or grades or documented proofs of work). I do plan to mention and elaborate on them in my PS but I worry that there isn’t a strong enough reason for Cambridge to believe that I’ve actually started on them. So, do I have good chances to get into Cambridge / what are some things I should do now?

I think the problem is more likely to be, based on what you've indicated, you've not at any point sat the exams for three A-level subjects in a single exam session/year. This can be a concern sometimes. I'd recommend checking with Cambridge if the format of how you've sat your exams is an issue or not.

Having S,S in STEP already is an excellent starting point though.

Not having IGCSEs is not an issue - they will assess you on whatever your 14-16 education was. They are used to assessing a wide range of qualifications.

Not sure what the relevance of your middle school studies are - in the UK middle school is normally considered to be years 7-9, and not considered at all in university applications. Only your 14-18 education is considered.

Also not sure what you're talking about in terms of transferring.

In terms of the personal statement they are just looking for evidence of your interest and awareness of the subject. They don't expect you to have already studied the course before you even start, although if you have been doing wider reading in those areas that's perfectly valid to discuss in your PS