There are a couple of important things to note here:
+ Your Masters Degree is not a limiting factor to decide if you are a good candidate. My colleage has a Masters in Religion and he got offers from 2 of the top Big 3. Your overall profile - experience, leadership, education, etc. - determines your fit for the interview. Post that, it's all about how you perform at the interviews - Are you good at structuring the problem and critical thinking? Do you have good stories that demonstrate Leadership? and so on.
+ There are many consulting firms that are diversifying their usual consulting track. For instance, McKinsey hires data scientists who usually have a data analytics background like yourself. Data scientists have a slightly different career track, but they are a part of teams where there is huge amount of data, limited time to complete analysis or the need to use softwares apart from standard Excel/Tableau e.g., Python. I worked with a data analyst on my team a few months ago and the impact was terrific.
Hope this helps!