Rejected without McKinsey Solve

Hi,
I had applied to McKinsey middle east region a while back after some conversations with consultants there but after the application I wasn't even given the Solve invite, which has always been the case in the past. I am also quite surprised at the rejection because I come from a good school Masters, good internships and had made sure to make a consulting style CV with pointers showing Action, Impact and Outcome. I am having conversations with some more senior Associate/EM level people at the ME offices and I was wondering would it be possible to reapply with a referral? I know that I can do well in interviews, and I had previously passed Solve game within a 10th decile scoring too, I would really like to get some guidance here