reapplying to Cambridge for maths

3 A*s and 1,1 in STEP are standard requirements.
It’s hard to see why a gap year applicant with the same profile would be preferred over a fresh one — unless they’ve clearly used the extra time to explore the subject further to stand out for the rest.
I would suggest to take part in math Olympiad or engaging in math competitions .
By the way are the an international applicant ?

no, I'm not an international applicant. I figure I would use the gap year to do something to engage with maths, but I don't really know what I'd do. I figured I'd stand a chance as a gap year student as I would have already achieved the required grades, and proven myself to be good enough, whereas a fresh applicant wouldn't be such a sure thing, but I don't really know if that's what they think too.

I applied to Cambridge for maths this year, I made it to the interview but was later rejected. A couple months later, I received an offer to study maths at Imperial, and as part of it they required a 2 in STEP 2 or 3. I decided to sit both of them to increase my odds of doing well in one of them. Now I feel that there is a good chance that I get a 1,1 as I have been doing quite well with practice questions/tests. If I got a 1,1 and A*A*AA in my a-levels, do you think I would get into Cambridge if I took a gap year and reapplied?
I applied to St. Johns if that's relevant.

So people do reapply and some are successful. I guess you have to be ok with possibly being rejected again and having a plan for what youd do instead / wasting a year. If so (and you want to), try again.
Have you asked about your interview/rejection? In keeping maths up during the gap year, obv youd need to do a bit pre interview and if you had to resit step youd need some work for that. Otherwise there would is no way they could force you / check up on you doing other maths post interview.

What subjects you are studying ? And is your school helping you to prepare for STEP ?

I'd be ok getting rejected again, I just figure if there's a chance I get in (a good one at least), I might as well try to. And I didn't ask for feedback on my application, so I don't know what was wrong with it, but the interview didn't go great from my point of view.

Its really your shout though Id ask for the feedback, even if its not great. They want to see whether you have a reasonble chance of passing step and how youd fit into the tutorial system they have (so are you "teachable"). Even if you didnt perform well, its worth seeing what they thought / what to improve on.
But there are no guarantees, even if you hit the step / a level grades and there are no guarantees of another imperial offer either.

Honestly, unless I get at least a 1,1 in step and 3-4 a*s, I won't even consider reapplying. it is possible, but its not the most likely outcome, I was honestly just wondering if there was a good chance I could get in if I got those grades and reapplied.