Advice on how to get started in consulting

Hello to all!

I've been reading this forum for a few weeks now, and the truth is that I've found some great tips that will be very helpful. 

I am a student of one of the top 20 Masters in Management in the world according to the Financial Times, in an university at Europe. I am writing this post because I am a bit lost, since I would like to focus my professional career on working in consulting, but it seems impossible for me right now...

I am not a great student, I have studied labor relations and human resources in an average Spanish university with a 7/10 GPA, and I have entered this Master's because of my extracurricular activities and my ability to write application letters. Although my college is targeted by BCG and McKinsey, I find it very difficult to compete with other students who have a better academic background than I do. Even for networking events organized at my university for small groups of students, I have been turned down by Bain and Oliver Wyman just by looking at my CV.

It would be very helpful if someone has experience and can share some tips, of how I should approach my career right now, since I am looking for a job for next year, when I finish my Master's, and I still don't have my Master's grades (as I just started the program one month ago) to send those instead of my Bachelor's.

Thank you so much!