Rajat,
I've worked with a few candidates with a healthcare background moving into healthcare or life sciences consulting. I'm happy to provide a perspective.
Most importantly, in order to make this transition, it helps (to a certain extent it's required) to have some relevant expertise in this area. That could mean having an actual medical degree, or a science-related degree or even a master's degree in a related field.
Alternatively, you should have relevant professional experience.
That's often the case with specialist roles, such as healthcare consulting. As opposed to being a generalist, you're expected to come in with some useful body of knowledge.
Best,
Cristian