Does Big 4 Audit make sense for me?

Nothing in my profile adds up but I still think you guys can point me in the right direction. I have done a bachelor's in Business Administration in a no name university (high GPA), some internships throughout uni. After graduating, I have worked in a boutique advisory firm. Basically, I did all sorts of things starting from data analytics with R to some modeling and valuation. In parallel with that, I have started my own business (Logistics coordination, unrelated with finance). I worked on my business at nights, as most of our partners are on the other side of the globe. I have taken the CFA Level 1 exam this December and am waiting for the results. If all of this wasn't confusing enough, I have an offer from LSE MSc in Finance program starting in September 2020. I am not working now and have a passive role in my business and have around 7 months until my program at LSE starts. I think I will be targeting IB and PE positions in London. What do you think would be the best way to strengthen my profile given my circumstances. I have an offer from a Big 4 firm to become an Audit assistant but am hesitant to accept it since I am not sure if it will strengthen my resume. What are your thoughts? Thank you very much in advance, I am really lost at this point and need some advice.