25 years old, no work experience - PE or Quant possible or a fool's errand?

I've looked through similar discussions, which have been immensely helpful, but I would like to gather information and guidance more specific to my situation - I already know that I'm going to have to network incessantly. This is my first post on here, so I apologize if what follows is erroneous or verbose.

Background: Since completing undergrad almost 3 years ago, I've been trying to make it in competitive gaming full-time. In short, I've been largely unsuccessful. Neither my team nor I has been signed to a professional organization or sponsored, so the little money I've made has mostly come from (inconsistent) tournament placements. I currently live in the Kansas City area. I'm not in debt, and if needed, my dad has graciously offered to help me get on my feet in the early stages.

Education: I have a BA in physics and a BA in English from a small, private, top 30 university (non-target). 

From what I have read thus far, it seems that my paths to either PE or quant are roughly the following:

1. PE - internship (ideally PE) --> work --> MBA --> IB (preferred) or consulting --> PE
2. Quant - internship (ideally quant) --> work --> masters in physics --> PhD? --> quant

Of course, there are other ways, but I'm interested in determining the steps that would give me the best chance in the shortest possible amount of time. Starting with an internship seems like a necessity at this stage. However, at 25, I am concerned that I'm too old for, what would likely be, an unpaid internship; what company is going to take a chance on me over a younger, college kid at a target school? Additionally, what would my realistic options be for work between the internship and masters? Please correct me if anything mentioned thus far is inaccurate or suboptimal. 

I know that PE and quant, while not exactly similar in terms of the actual work, are both fiercely competitive. I also know that my situation is far from ideal. Nonetheless, I am genuinely interested in both careers and am highly motivated to put in the requisite work to break into one of them.

Thus, which option is more doable? Are there better or comparable routes that I should be considering? Any general advice is welcome as well. 

With all that said, I hope I don't come across as feeling entitled, or even confident. While I am confident in my abilities, I understand that, given my situation, I have no justification for believing that I will successfully reach either of these goals. If I need a reality check, then please don't hold back.

Thank you all in advance.