No. You do not need a referral to receive an interview at McKinsey, BCG or Bain.

Candidates are hired through normal recruiting channels without referrals every cycle, including advanced-degree candidates.

A referral may help visibility or provide context, but it does not replace the firm's screening and interview process.

Apply on time with the strongest application you can build; do not delay a deadline while waiting for a referral that may never come. For more detail, see the PhD networking guide.

yeah, Alumni were much easier to approach than completely random consultants.

For what it's worth, I would not make the referral the goal of the first call.

A short follow-up is fine. Repeated follow-ups started to feel awkward for me.