How to increase chances of getting into a top uni?

I'd like to study computer science at Cambridge or Oxford (preferably Cambridge). I'm thinking about moving to America and studying at places like MIT, Princeton and Stanford too.

I'm from Scotland and assuming I get all A's on my highers - Physics, Chemistry, Maths, English (only taking 4 because i'm studying for an HNC in computing at college too) and all A's on my advanced highers - Physics, Maths (Still taking the HNC at this point, will finish it this year) do I have good odds of getting in relative to the average applicant?

What can I do to boost my chances of success? I'm aware I need to take SATs or ACTs for admission into American universities. There aren't any programming clubs or anything like that around my area.

An HNC is equivalent to an advanced higher for anyone who doesn't know.

I don't know much about US unis apart from the fact that you also need to have amazing extracurriculars apparently to get in. But in terms of Cambridge and other UK unis, I would suggest doing lots of maths, as computer science degrees at top unis are often quite focused on theory, so they mainly test mathematical skills in the admissions tests and interviews.

And you don't need a programming club to program, computer science is one of the easiest subjects to get started on your own because there are tons of resources online and it's quite easy to create a project on your own. You could also look into maths and computer science olympiads, if you're into competitions. But yeah, for Cambridge just focus on getting good grades and do stuff in computer science and maths that interests you.