How would you start your career as a consultant without a degree or relevant experience?

I think you have two main options:

1. Most commonly thought of in here, you convince a consultancy to give you a shot, largely by showing them you have a history of being an overachiever, albeit in non-traditional fields (medicine, legal, arts...). Best then to also prepare for a case interview, which is the whole purpose of this site. If this is what you are looking at, we can help

2. Less mentioned here, you can just start your own company and slowly build expertise over time. Someone I know this built a following in just over 12 months doing social media / marketing consulting on the web, leveraging such platforms as fiverr and basically learning on the fly. He made no money for some time, but now well on his way to being independently wealthy because he kept at it and put in the work

Which option are you thinking of? We can dig a little deeper then.