Hello and thanks for your post.
The application process is truly holistic, and committees will look at your stats (GPA and GRE), work experience, and extracurriculars.
Your GPA is strong, so that is a good start. Your GRE is also very strong, though compared to others in your demographic, it is about the average. If you haven’t already, I suggest taking it up to 3-4 times. You have nothing to lose since schools will only look at your highest score. And even a slight increase can boost your profile.
It is hard to gauge your work experience without knowing your accomplishments and impact you have made there. It is nice to see that in general you have had three promotions. In order to stand out, it will be important to show you have made an impact and demonstrated leadership there. Ideally this will be supported by strong recommendation letters as well. It will also be important to explain why you want your MBA, and to also illustrate the skills you already have which are transferable to being in product management. Be sure your story makes sense, and is realistic and specific.
Regarding extracurriculars, make sure to really emphasize your leadership roles you have taken on. Working with an NGO certainly sounds impressive, though ideally you will have done that after university as well.
I would say to apply to top 15 schools as your reach/target schools, perhaps those consistently ranked between 10 and 15. You should have a chance at some of these schools, but they are extremely competitive, and each school simply does not have the room to admit all the world's qualified applicants. For that reason, I suggest apply to some other schools that are ranked slightly lower, yet are still really strong programs with global brand recognition. Figure out what your “tipping point” is – which schools you would still be excited to attend, even though they are not ranked as high. And hopefully they will see that you have a compelling story and are someone who will add value to the classroom and community.
Good luck!