Should I try for jobs that demand work ex in the description

Unless the recruiter on the other side has this soft mandate that candidates from top tier institutes can be considered, it might end up in rejection. Always feel free to apply :)

Usually as a fresher it's okish to apply for jobs requiring 0-3 years of experience. But if a job is asking for like 4+ minimum then they are definitely not looking for freshers regardless of your skillset.