Actually, research isn't a
critical part of medical school admissions decisions. It certainly would not hurt and can only improve your application, but in actuality volunteering and clinical experience are valued much more highly. See here:
https://www.aamc.org/download/434596/data/usingmcatdata2016.pdf (Table 1, p.3) Also take critical note that it all pales in comparison to how important GPA and MCAT are rated. Your first priority above all are grades, grades, grades.
Research experience is of medium importance for private institutions, and of low importance for public institutions. I'm not sure if you'll have time to do both research and volunteering, but if you have to prioritize one or the other I would suggest you definitely find some kind of clinical volunteering experience, especially since you say you have done exclusively non-medical related activities. That shows adcoms that you have experienced what it's like to be on the floor with patients and you're not jumping into the field unaware of what it's really like. Research is great because you can get a better appreciation for how advancements in medicine proceed and better understand the data behind new clinical trials etc; however, it isn't as reflective of what the job is like in comparison to being on the floor with physicians, nurses, and other caregivers. It speaks greater volumes if you choose to volunteer your time with people helping them even if they're yelling obscenities at you, rather than in a quiet lab where you're removed from most social interactions.
But if you can do both, great! Regarding research opportunities, I would first suggest you establish yourself by doing well (As) in some of your classes, like chem/bio/ochem and especially any lab classes. Biochem would also help. With no science background, it would behoove you to have something under your belt first as proof you're capable before labs take a chance on you. It would also give you the background necessary to understand some of the things they're doing, otherwise it's going to be very difficult for you and for the lab to try to teach you.
Don't get your hopes up about publications either. They usually take more than a year to gather all the data and then a longer time to go through the review process, and it's going to be very hard going from absolutely zero lab experience to being able to contribute at the advanced level where the scientific community will take you seriously enough to publish you in a short amount of time. Generally takes like 2-3 years of research experience.
Your best in is with the professors of your classes. If you do well in the class and get to know the professor, you could ask them if they would be willing to take you on in their lab (assuming the prof has a lab - look that up beforehand). See if there's ways you can take advantage of Harvard's career center and find out about any openings or opportunities in labs. Do a lot of googling for bio/pharma institutes that offer internships. You can also try e-mailing professors at Harvard/BU/wherever, kind of like cold-calling clinics for shadowing opportunities. And when contacting, I would also suggest reading up on what lab does and reading one of the papers they published. That shows real interest and will make them more receptive to you rather than "hey I'm a premed trying to get literally any lab opportunity can you take me".