There are many different ways to get into a big 4 after you start your career. The best thing you can do to make working at a big 4 happen is to have a plan. When having a plan you should consider what area at a big 4 you are interested in. I would recommend going through the web pages of the big 4 firms and finding an area that interests you. It sounds like management consulting is something you are interested in based on your hashtag and this is a career that is very broad with many people from different career backgrounds. Your path should focus on getting experience within the consulting industry at other firms and then tailoring your experience within your first few years of being in consulting towards the career path you found when researching about what the big 4 do.
Taking control of your career and guiding yourself towards a goal will help you to achieve breaking into a big 4 firm. You can discuss career plans with those around you (friends, teachers, mentors, etc.) and network your way into a discussion with someone who works at a big 4 firm. Ultimately, having a plan about where you want to go will help you take ownership of your career and will most likely answer the question of what to do now to get to where you want to go.
Ana recommends the following next steps:
I work in a Technical role with an undergraduate degree in English and Philosophy. Your background is less important than what you are willing to learn through experience in roles.