Questions regarding transfer student SAT scores & letters of rec

I am a freshmen looking towards transferring from my four-year and had a couple questions regarding the said two topics. Now I already did my research for my target schools and am not asking if I need them or not but rather their impact. All my current classes right now have rather large class sizes of at least a minimum of 50-70 and an upwards of 100+ students per professor. Point being, I don’t think it’ll be worth asking any of them for a letter of rec as I have searched and am continuously looking for ways to personally connect with them. And before you give me suggestions, yes, I have already checked if they are doing any research or have available positions. Yes, I have checked if I can schedule meetings with them but they dump it all on the TAs. And best of all, they don’t have a lot of opening during or a bit after class as all of them lecture and have immediate classes right after. I know I should technically already know my answer but any suggestions?

Another point of consideration…
I will have eventually allocated 56 credits total by the end of my freshmen year thanks to AP transferable and such. Point being, do you think it’ll be better to apply as an upcoming sophomore or junior if I had the choice? I know some colleges depend on how many core/GE classes you have covered to be considered for either but assuming I had the choice and fulfilled the credits equivalent to a junior (which for most colleges is 60 to my knowledge), as I’ll probably take classes wherever I transfer if possible, what do you think? Some colleges I can get past not sending the SAT with this or maybe even my letters of rec but I wanted to know if there is anything underlying.

(Please no Q’s about why I am transferring, I like Purdue and wouldn’t mind staying at all but there are obviously more complicated reasons)

Some information if needed…

My school: Purdue University - West Lafayette (Main Campus)

Transfer Targets(in no particular order): UC Berkeley, UCI, Boston College, NYU, U of Michigan - Ann Arbor, Northwestern, Vanderbilt, USC, UCLA, Cornell

Intended Major for transfer: Business Admin. if available or Economics & business related majors (for schools without a college of business)

Expected completed credits by end of freshmen year: 56

My personal guess of GPA: 3.65-3.9

My previous SAT score from HS: 1350