Industry Lateral Process

Hi Everyone -

I'm currently an FP&A Analyst at one of the super majors in the oil & gas space, and as of late my interests professionally have crossed from purely financial to more operational/strategic. Unfortunately, within the O&G space, most strategic roles are limited to engineering backgrounds, and thus there is a ceiling on what a pure finance person can accomplish long-term. I want to learn how to run a business, the thought process behind strategic decisions, and how to execute on business plans. And thus, in my mind, a pivot to management consulting seems like the most logical fit. That being said, I'm not sure how to actually get my foot in the door outside of attempting to LinkedIn cold messaging. An MBA is a possibility, but preferably would be the last choice due to the opportunity cost of leaving a decent job for grad school and no income for two years.

My question to you all is: any ideas on what to do other than continuing the cold messaging process? Any additional items you all suggest that have maybe worked for you before? Any advice you have would be appreciated as I try to make this pivot.

As a reference, I've listed my background below to help address some of those questions.

Geography:
-South/Southwestern
Undergrad:
-Regional, large state university, non-target
-Finance BBA, Public Relations Minor
-3.95 GPA, multiple honors and extracurriculars
Grad:
-MSF from regional semi-target
-3.96 GPA
-Graduated #2 in class and was on leadership of several committees
Work:
-Started at F50 E&P in Finance Development Program for 2 years, multiple assignments
-Left for MSF after 2 years, and started at small L/S equity fund as co-op and then full-time (total of 1.5 years)
-Went to work for IOC and have been with company for just over a year; ranked in top quintile of analysts globally
Other:
-CFA L3 Candidate