Yes, you can switch career in management consulting prior an MBA. Hiring for consulting firms happen during off-campus recruitment drives. So, in case you want to switch into management consulting, there is no need to start your MBA application with the intention of getting into an on-campus program. You can start applying from any of the management consulting firms before or after your career as a consultant and also at different points in your life!
You need to keep in mind that there are many ways in which you can switch your career in consulting. For example, if you have tried to get in a consulting firm via on-campus recruitment drives but could not, then one way is to try an off-campus recruitment drive/lateral hiring. You need to keep an eye on LinkedIn and check for all the latest postings there by any employee at a consulting firm! Do check how far back does the company go into recruiting people as well? Also, see if the firm gives preference to those who have had experience from industry specific courses or training courses.
You can attend the course here - https://www.seekho.ai/courses/management-consulting/CT-131-31409
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. :)