Establishing a financial career with BSc @ Johns Hopkins possible?

Hello!

Currently I'm a junior at Johns Hopkins, majoring in CS and Applied Math & Statistics. Though I'm on my way to becoming a SWE, meeting a lot of high school peers who goes to Penn or UVA & going to finance electives has kinda piqued my interest into pivoting into finance. I know there are quant shops and everything, but seems like quant roles are very few and far inbetween, and most of them require at least a MS. (Also, JHU isn't great at placing to quant to begin with, i think)

However, JHU is not really a target school for top Wall Street firms, it seems - there's minimal OCR, and lack of alumni at IB firms according to LinkedIn; with a lot of them being SWEs or other back office guys. I know Wall Street firms place school prestige higher compared to other industries -- especially compared to tech -- so is it possible to land a front office role? Or should I finish my BS and get my MS at some target school by majoring in finance?

Additionally:

• How can I network if there's very little alumni that goes to Wall Street firms? Is messaging alumni from Wall Street firms via LinkedIn just plain weird?

• Do SWE internships at financial institutions help your resume? i.e. SWE at MS; or are back office experience not really regarded as good?