If there is a clear deadline mentioned in their website which says if you cancel enrollment you will get refund within X date, you can claim refund if you’re still in that date. but now it’s 7th of Feb and you most probably missed the deadline.
But even in this case, some universities usually refund at least 50% after starting classess when its still not too late.
Now, if there is clear mention about the policy you can ask them to refund the money (deducting some administrative fees 500-100 usually).
But every university has some sort of policy maybe you haven’t found that on their website & typically they dont flash these kind of information to user that easily. its business nonetheless.
So if they can provide any sort of evidence supporting their non-refundable policy, the chances of getting refund is very slim.
keep talking with university officials and see what happens.
let us know what happens.