No, you are definitely not too late. Making a switch in fields is not uncommon. However, since you are from the medical field and currently don't know much about consulting, it will be advisable to connect with people from the consulting domain. The next step would be to look for opportunities on different job portals or through personal connections and finally preparing for the interview rounds.
For getting in a Consulting Firm through off-campus recruitment drives-
Consulting Firms do hire via on-campus placement drives is true but they only hire via on-campus placement drives is not. Mostly all of the consulting firms do also have off-campus recruitment drives/lateral hiring going on throughout the year.
For the same, keep an eye on the LinkedIn job portal, their career pages and LinkedIn posts by the employees at these firms. One thing that could help here is tapping people for referrals!
Since consulting is more of a 'Generalist's Job', experience in any and every industry would be relevant and in fact, diverse industry expertise is always better for the firm!
Besides, it is never too late. :)
I don’t think you are late. MBBS graduates working in consulting isn’t unheard of. However, it wouldn’t be easy to switch considering your prior work experience. I’d suggest you to network with a few professionals in the management consulting space in order to get an understanding about their work, and how you can benefit them using your existing knowledge. You could also try for an MBA which would assist you getting a job in the domain with the least possible friction.