People like me usually make friends and discuss about math with people who are also math olympiad enthusiasts from that site, but how to do that ?
My initial thought is that you got this backwards. Some people are friends IRL with an interest in maths and if one of them finds a site like AoPS they'll tell the other so they can both explore it together.
Also, some guys make friends on that site by discussing problems and sending each other problems to work on
How do you know this? As far as I could tell at first glance the entire site is based on posting interesting questions on the forum and let people post answers to them there. That doesn't look like it's an easy way to start friendships.
It does sound like a really good way to fullfil that craving for interesting math problems. Similarly to how I'm interested in finding out about interpersonal issues and how to deal with those (which brings me here).
Since the more logical step to make math-friends would be to start IRL I was a bit confused about your first couple of sentences:
but unfortunately no friend of mine in my school/city is really interested in maths.
From this I conclude you do have some friends with some common interest, just other than the math. Since you can satisfy your math craving on that site, aren't those friends enough?
If they're not, then I still find this statement a bit odd:
And going to any math club is not feasible for me due to I having a weird timing slot.
How is it possible for the other people in that math club but not for you? If you're really only interested in math, how could it be so hard to make time to join such a club? Since that is exactly the place where you want to be (based on your question here).
Let's finally assume that I'm wrong in the previous parts and that you really do want to find an online friend via that site. Try looking at it this way then:
You're sure that (based on which sub forum you're looking at) you and the other people replying to your questions (/ you replying to theirs) are having a common interest. How can you go wrong with sending them a personal message like this one:
Hi < future friends name >, I noticed you've been answering a couple of my math questions and I've had fun solving yours as well. I'm looking for someone to have some more direct discussions with about these kinds of math problems. Are you interested as well? Hope to hear from you soon, Alex K Chen
If they're interested they'll probably respond soon after seeing your message (i.e. within a couple of days). If they're not they'll just ignore the message altogether.
Just look through a couple of your questions/answers to see if you start to recognise some recurring names of other math-enthusiasts there and send them a message like this one :) Who knows you might prove me wrong and make a great friend online like that.
Last remark: the questions I ask you in this answer are purely rhetorical. Their purpose is to make you think about it yourself rather than answer them to me.