Guidance regarding entry level product roles

I'm an aspiring APM/Product Analyst from a Tier-3 College in India I have built a comprehensive portfolio comprising Product Teardowns,Case Studies, Guesstimates, Side Projects and PM articles I've been cold DMing PMs on LinkedIn but the response rate isn't high(People aren't reading the message I'm sending with connection request) I need guidance to get at least an internship for summer 2024, so that I can get a PPO later on

PS: I'm a 2025 grad