Sophomore at a non/semi-target -- give up on IBD/S&T for this summer and go for a PE/HF/WM role?

I'm a sophomore, prospective finance major with a 3.9 at Penn State. Most consider it a non-target, although Goldman Sachs, BAML, and JPMorgan do OCR now. Regardless, I was wondering if I'd be better off trying to get a summer role as a PE/HF/WM intern this summer. I simply don't have the network nor the "brand name" school on my resume I feel like one would need to get an IBD/S&T internship this summer. I applied to a bunch online nonetheless, but I haven't heard back and don't anticipate to.

So then what confuses me is exactly when recruiting season starts for PE/HF/WM roles, and what the process is. I've been reading November through January/February. I've also read that securing an internship is mainly done through cold calling/cold e-mailing. Should I start to network now? When should I start to reach out to these firms? I lack good guidance at my school -- my career advisor is kind of shit honestly. I'd appreciate some advice. Thanks in advance.