Thinking of leaving for something better, lateral the right move?

Hey fellow monkeys,

I've been at an entry-level consulting-related role since the start of this year at a firm with a good reputation. For context, the firm is well-regarded (top 20-30, 2000+ employees) but has been operating under a "senior-heavy" model for most of its lifespan. Quite recently, they began hiring undergrads into an entry-level 2-year research role to prepare us for their actual consulting roles, presumably because they don't trust that kids out of college can do the job right away. Since I started, my job has involved responding to requests from more senior consultants who either need ad-hoc help on an engagement or need assistance on a pitch. In short, we (the researcher analysts) are never actually staffed on an engagement but instead help out whenever it is needed, mostly by providing data.

The role is very independent to the point where I can have zero communication with management on any given day (this has lasted weeks sometimes), and I often have to find things to keep me busy if we don't get sent anything from consultants on the field (especially slow during summer). I do collaborate with the other analysts though, which is the only good thing about the job. The problem is that I've noticed this team (research) isn't very valuable to the overall firm and isn't teaching me the necessary skillset to prepare me for the eventual consulting role. It seems that even the Directors don't care too much about the program and are happy with how things are given the incredible flexibility the job offers (there is minimal oversight, I've seen some leave at 2pm sometimes and they often work from home). There is so much more to unpack about how crazy and absurd this team is in relation to the firm but I wouldn't want to write even more. I actually feel that I am less qualified than I was when I recruited for consulting roles out of college.

I have been wondering for some time whether I should lateral to another consulting firm that actually teaches junior professionals important skills and gives them early client exposure on an actual 1-4 month engagement (think MBB). I know a lot about consulting as I read, practiced cases, and networked heavily during/after college, but am also an international student on OPT (which expires in 2 years if I don't get approved for H-1B). Is anyone familiar with top 10 recruiting schedules and if there's any way to spin this, and if they would entertain a candidate like me? I don't want to wait another 1/1.5 years until transitioning only to be known as the "research guy".

Sorry for the long post. Would be grateful hearing any advice or thoughts you have on the situation. Thank you!!