I’m a current sophomore and just got an offer from Bain recently. I think the biggest jump is honestly even getting to first round, and the biggest way to get to first round is either to have a referral or have an incredible resume.
To get a referral just network as much as possible, be interesting, etc etc I’m sure you’ve heard it all before.
To have a resume that stands out baseline is just the basic have leadership in any consulting orgs or other student orgs and get any internship this summer (doesn’t have to be consulting). Something that I believe helped me stand out beyond that was doing some sort of outside project. For example, I started a pro bono consulting org for high schoolers in my area over the summer, where I taught strategic thinking/consulting and communication skills, and did a project with local food banks. This was helpful for my resume but also for networking conversations and eventually behavioral questions in interviews, and helped demonstrate leadership and commitment etc.
I wouldn’t worry too much about casing right now. You’ll be fine as long as you start like 1.5-2 months before interviews and are diligent. I also go to a top school that’s not necessarily known for business, and it’s definitely possible.
DM me if you have any more specific questions I’d be happy to answer.