Can I do CSE without JEE?

I want to pursue a B.Tech in Computer Science Engineering (CSE), but I haven't appeared for JEE Main. Is it possible to get admission to a good engineering college without JEE? Which colleges offer CSE based on Class 12 marks or their own entrance exams? Please also suggest some good private and government colleges, along with the admission process, eligibility criteria, fees, and placement opportunities.