Networking: How to for peds

Hope someone can help me out! I don’t want to be the weirdo who hands out business cards, but I wondering how to network. I currently work at a big hospital in Florida as a paramedic. I’ll be graduating with my ASN in April. I heard that our school has a hard time getting any good practicum slots, and it’s mostly limited to adult med tele/med surge nights. There were 6 spots in peds last semester and 36 applicants. My professor told me I might be able to get a pediatrics practicum if I can find someone to request me. I had a 4.0 GPA until my med surge class which I expect to get a B in. I know I won’t be able to start in pediatrics at this hospital after I graduate because they require a bachelors which will take me another year, but I would still like to do practicum with them or another children’s hospital if possible. Any advice?