How soon is too soon?

I literally just started a new role doing sell-side equity research for a very very tiny boutique a month ago, in a sector I have prior corporate experience in. In the last couple of days, a major bank posted an associate role in the same sector, and i’m truthfully interested. knowing that ER is so dependent on your Analyst and my longer-term career goals would be benefitted by being at a bigger brand name makes this role really appealing. 

my question to you all is 1) is it too quick to think about leaving my current gig for what could be a really huge upgrade and 2) assuming circumstances outweigh the short stint, how do I go about even doing this? do I leave this gig off my resume? do I try and network with the analyst? what’s the game plan for this kind of thing?