Applying solely through LinkedIn won't help you. Reach out to people for referrals and message recruiters as well. Also make a profile on naukri/monster/instahyer.
I agree with you about rejection, not every company bothers to send out one. Accept it and move on , we can't change their culture.
Referrals are the only ones that work , all my seniors tell me that referrals are important , they get you to the interview , after that it on your skill.