Specific Consulting firms target specific backgrounds?

Hello! I am a current rising senior at a good US school (think Patriot League, NESCAC etc.). I am studying Economics and Data Science, I am pretty heavily involved on campus (I’m a D1 athlete , I am head of a few clubs/committees, I am also very involved in the community) and I also carry a 3.4 GPA. Past summers I have worked as a finance intern for asset management firms, but this summer I am doing something actually completely different. I am working for a tech start up remotely as a data science and machine learning engineer intern. It’s super interesting and I love the work I do. Originally I was supposed to have a much more finance based internship but the group I was supposed to work with had to cancel because of COVID, so I worked hard and quickly found the role I’m in now. The reason I am posting is because I am pretty interested in pursuing consulting after graduation and I was wondering if anyone had any ideas what would be the best way for me to go at it and if there were any specific routes or firms I should target more based on my background?Most people I know who go into consulting have an internship where they get a full time offer after and that’s how they break in. I know I might not have the traditional background but would that hurt me? Thanks