"No-name" boutique 1st year - lateraling to MM/EB/BB

Background - come from a target, medium-ish GPA (mid 3.6s, albeit major GPA in mid 3.9s). 

Started work at a "no-name" regional boutique this summer (had no IB SA to work with in the summer prior so options were rather slim for FT - extremely grateful to be in a position I'm in right now). Had no formal training, got immediately staffed on a few live deals; Learning curve has been steep but rewarding thus far.

That said, I know that I want to lateral in the medium-term future, ideally within the first year and even moreso within this calendar year (i.e. would love to conclude by Feb 2023ish); Motivations don't revolve around exit opps as I am on OPT and will most likely come back home after the Visa expires. Main driver is to garner experience working in a larger organization that would allow me to relocate if I decide to do so once I come home. 

Having read Sil's lateraling guide as well as a few others, I haven't yet found an answer that would address how should one position him/herself for a solid lateral position from the get-go. I know that it might sound ridiculous for one to seek lateraling this early, but knowing how long some of the processes go, I am certain that it's better to be too early than too late given my current situation and goals. 

A few direct questions that sit at top of mind are:

How should one approach networking to have people reach out to you once a spot opens up (can't really be explicit about wanting to lateral so early IMO)?

When should one start following-up with their network to best position for a Dec/Jan/Feb recruitment initiation process?

How should one approach technicals' prep to not burn out/forget things by the time they are needed?

Any input is highly appreciated.