Hi,

You can enter the consulting company at any stage. There might be many factors that might have influenced the decision when you were a graduate:

1. University brand
2. Internships you had before
3. The office you are applying to (Competition, Languages, work permit, etc)
4. Extracurricular activities:

• Launching your own venture and entrepreneurial activities (even failing them is fine)
• Grants / scholarships - even better if related to some research or entrepreneurial projects
• Projects for companies - you may consider doing a free project for the company or a startup or writing a case that future grads will use
• Volunteer / social activities. I would aim at the activities where you can have a leadership role. Organizing some club may work as well.
• Case Competitions-especially the ones organized by your target company
• Researches / articles published in well-known sources

Now, as far as I understand you still don't have that much of work experience so you will be assessed both by your graduate activities and by your career moves so far:

• Brand of the company
• Career growth and achievements
• Postgraduate extracurricular activities

It is hard to asses in detail without seeing your resume.

Best,