Advice for Breaking into IB 3 months after Graduation?

Context:
Went to a target school and received multiple interviews at pretty legit bulge bracket and large boutique banks, but I failed to secure an offer at each. This went on until I finally graduated this summer in 2018. Didn't want to be unemployed for too long (didn't want to be seen as "damaged goods") so I settled for a pretty decent job at a large Fintech firm. Main concern and reason I want to leave is because I'm not getting any legit training, so I feel like I am stagnating while my peers in IB or consulting are really growing and learning.

Questions:
1. Do banks require new hires to actually have previous modeling and IB experience in the past?
2. Should I list my 1-2 month experience in Ops on my resume? Didn't really accomplish anything here yet, but I also don't want the employer to think I've been unemployed for all this time.
3. When networking, should I mainly focus on reaching out to MDs, VPs, Associates, or Analysts?
4. Any other suggestions you guys might have that would make the early career transition more smoothly?

Thanks everyone!