Industry-Internal consultant(Engineering) Transition to Consulting

I've seen similar threads related to this but none specifically answer my questions so I wanted some advice. I work in healthcare(2-3 years experience) and I'm about 1 year into my new role which I've realized is very similar if not identical to the role of a consultant(internal). We work on business systems so a lot of our projects are linked to financial outcomes which led me to learning about this whole world of consulting/MBB/MBA pathways. I think this would be a great route for my career growth and seems very interesting, however I'm unsure about how to go about the transition. I plan to stay in my role at least 3 years(401k vesting) but while the exposure is amazing there is not much growth potential within the department, and tuition reimbursement is very low. Not sure if it's feasible to get my MBA while working here, but I'm not sure if I even need an MBA if I come in as an industry hire(5 years) with directly correlated job experience. Long term I am interested in operations and/or strategy so maybe an MBA down the line(job sponsored) is preferable, but for now, is it possible to get into a good consulting role without an MBA.

Other Considerations:
-Already making low 6 figures(However no bonus, and only 3% annual promotions)
-Good work life balance(830-5)
-Exposure to executives, and great projects
-Low tuition reimbursement

Essentially I don't want to give up my current position for a consulting job which will not be comparable/compensate my current role, and I'm not sure if I will get that without an MBA for a top school.