When to start networking summer 2022?

Start right now! Maybe start out with regional banks/banks not on your target list to get used to talking to bankers. Maybe I'm just an international but it takes me about 30-40 calls or so to get "comfortable" without sounding like I'm just rambling off a list of questions. Start early and follow up with them every 1-2 months or so and make the ask when application opens. Recruiting starts earlier than you thought.
 

Agree with everything above said ^ never too early to start!

Now.

I think the people saying "never too early" are right to some extent, but you are too in your concern that it's harder to start a connection now and maintain it 4-6 months. I'm a college junior so I just finished recruiting this past year, and I honestly didn't start networking with bankers until January. Sept-Dec I was focused mostly on coffee chatting upperclassmen at my school, and prepping behaviorals/technicals (starting in Dec winter break). I think starting with upperclassmen is incredibly helpful, because you can start to get a feel for each bank without the pressure of messing up a banker coffee chat. ie I got away with asking some dumber questions that I'm glad I never asked an analyst/associate. 

They were also helpful because if I hit it off with a senior (who interned at XYZ bank and was returning full time) they could refer me to analysts at the bank, and being able to say "hey I spoke with Name and he/she mentioned you" made my email response rate higher than I think it would've. Just something to keep in mind, totally up to you and I agree it's never too early. Just make sure you're ready to network because you don't want a dumb mistake in December to bite you in April of next year

They will only forget about you if you dont keep a line of communication. Forget the whole "I must network for summer SA" network to with bankers to build genuine connections and if they can help you get a SA gig then it's just a plus. You never know how those people can help you in a year or 2 from now.

I'm like 15-20 calls in with bankers from EBs/BBs