Suppose say my friends graduate at the age of 23-25 from a tier-1 nlu and join straight to Big 7. On the other hand , I do LLM abroad and join the big 7 few years later. Will that person who joined earlier than me be promoted to partner quickly? Or if I show my skills and overtake him/her in performance , I will be promoted ? What matters - performance or early joining?

Getting on 'Fast track' is difficult but not unheard of. It also depends on factors beyond your control - the chief amongst them being business requirement of the firm for one more partner.