I am writing this as a student from the University of Auckland who received a grad offer at BCG and also interviewed with Bain (final round) . As your question is more around getting an interview, I will not discuss on how to do well in a case interview (There is A LOT of resources for this online).
Now, firstly getting a job at one of these firms is not easy and I know people with amazing grades, many extra currics and great personalities who did not get an offer. However, I also know of people with worse grades, less impressive extra currics getting an offer. So never be disheartened if things don’t work out and there are many other consulting firms out there. The most basic requirement is to have a killer CV.
Anyway, the big 3 pride themselves on the diversity of their staff, so you can study pretty much anything and have a decent shot of getting in. Alumni range from med students, music grads to army officers. From my experience at UoA I feel as though there are three main that you will need to land an interview (This list is not exhaustive) .
1 - grades, 2 - extra-currics/leadership and 3 - Work experience.
GRADES: Since UoA is not a prestigious academic institution you definitely need higher grades than those coming from Ivy leagues, oxbridge, IITs etc. However, there is no “threshold” GPA. For example, a BE (Hons) conjoint or an LLB conjoint student would not need as high of a grade as a simple BCom student. Regardless, you will need to be in the top 5-10% of whatever you study for them to consider you as a serious candidate. Things such as First in Class awards, deans list etc are good ways to stand out. If you’re doing just a BCom a minimum 8.25, ideally 8.5+.
EXTRA CURRICS/LEADERSHIP: This one is difficult. You need to show that you have shown initiative and excelled in something outside of study. If you want to join a club, definitely join MCC and complete the development program. This is run by Brendon Potter and really does set you up well for the case interview. It is also common for students on Student government positions to get interviews, so if you’re sociable and are confident that you can make an impact and get elected run for a student society leadership position. Otherwise, find something outside the classroom and pursue it. Social issues will generally get extra points, but again don’t join a charitable club just for your CV. You need to show that you have made an impact and are passionate about what you’re doing. Things such as sport, arts and other activities also come under thus umbrella and you need to show excellence and commitment in whatever your extra curric is. Leadership is the most ideal attribute they will look for so make sure you tickets that box in whatever extra curric you do. For getting a job at an investment bank, join UAIC, BAP and land an exec position. This shows them that you’re a serious candidate who is passionate about Finance.
3-WORK EXPERIENCE : This probably has the least or most weighting on whether or not you land an interview, mainly because BCG encourages people from 2nd and 3rd year to apply for the grad roles. However, an internship at a reputable firm will definitely help. I haven’t heard of anyone who did an IB internship and applied for BCG and didn’t get an interview. Again, sometimes these internships are just as difficult to get as a job at the big 3.
This work experience also doesn’t have to be related to consulting/business. For example, if you study compsci or engineering and did an internship at Google that would be more valuable than a stint at KPMG. Entrepreneurship is also a good skill to show, however don’t come up with a business just for your CV.
Finally to answer your last question. It’s absolutely possible to get in from UoA and many students get in each year. If you wanna pursue further education, do it for sure!
Hope this helps and best of luck!