As others have said, don't be too focused on getting into one particular school. There is a bit of luck involved in admissions to any one school(especially to a 'top school' like Columbia). Interviewers, even at the same school, don't always look for the same things. At one school I was interviewed by two MPH's and both interviews focused heavily on healthcare policy--which I have no experiences on. Other interviewees did not experience this. So, if you happen to get an interviewer with whom you have nothing in common, you might be out of luck. Also, your "dream school" may change as you learn more about them, especially during the interview day. Certain schools that I thought I would really love to attend fell flat while others really impressed. Who knows, a school you currently could not imagine going to could end up being your top choice in a few years
🙂.
With all of this said, there are certain things you could do to improve your chances of getting into a "top" school.
1) Good GPA, MCAT and LORs are pretty much musts. Get to know some of your professors well so that they can write personalized and supporting recommendations for you.
2)
Meaningful research experience is also looked upon favorably from what I've seen. A publication is absolutely not necessary to gain acceptance to a "top 10." But you definitely need to be able to talk about your role in the research. The key imo is to show potential.
3) Engage in activities that are meaningful to you and do them well. You want your application to paint a consistent and genuine picture of who you are. You do not need to go to Africa to volunteer or to start your own clinic, etc. in order to be admitted. Even if your EC activities are standard (e.g. hospital volunteering, teaching, etc.), that doesn't mean they are boring/cookie-cutter (it only will be cookie-cutter if you're just going through the motions with them imo). For example, when you volunteer, make an effort to get to know the patients instead of just getting them water/blankets. Likewise, if you're a TA, actively try to help your students succeed, especially the people who are genuinely struggling with the course. Being able to reflect and write thoughtfully about these experiences will speak volumes about you, much more so than simply listing being President of a do-nothing premed club.
4) Have interests outside of medicine. One interviewer chuckled as he told me about how many people listed their hospital volunteering, research, and premed club (the premed trifecta if you will) as their "most meaningful" activities

. Don't be one of those people.
Also, it might just be me, but I got the vibe that P&S seems to really like artists, musicians and performers. The med students I met there on interview day seemed to have these artsy talents.
With all this said, keep in mind that even though ECs are important, GPA/MCAT/LORs are much more important. IMO, there's a lot of SDN hype about the importance of having "unique" ECs ("you'll never get into a top school without unique activity X"
🙄). From my friends and my experiences, numbers and LORs seem to matter a lot more when determining who gets interview invites and subsequently acceptances.