How much is sufficient netorking?

Typically, what is a sufficient amount of networking at a bank that one should have to pretty safely get a first round? (# of people, levels of seniority)
 

and should networking at a firm by complete by the time of application to be able to actually help you, or is it still possible to get a first round if you haven't networked much when applying but continue to do so soon after?
 

I'm just quite behind on networking and now realizing I should've been doing it in the late fall instead of now. Almost everything is open but I've spoken to only a few people or even none at some banks, and I don't want to wait too long too apply otherwise my application will get drowned out with everyone else.

any tips? (I'm at a target school if that means anything)