Product roles at LinkedIn?

I’m a recent grad (May 2018) with a year of experience, and I currently work as a product analyst elsewhere and am looking for product management roles. I genuinely love LinkedIn as a product and would love to work there, but seems like I missed the boat by not applying to APM last year - any advice on what I can do now? What’s the next entry level after APM for Product at LinkedIn (2/4/? years work experience?), and what can I do to prepare myself as a competitive applicant in the interim? Appreciate all inputs - thanks!