Yes, diploma students can apply if they have Mathematics and also if they join first year.

For more details read - NATA Eligibility Criteria

As per the eligibility to apply for NATA Entrance Exam, You must have passed any of following exams:

10+2

10+3 Diploma (any stream)

International Baccalaureate Diploma after after 10 years of Schooling

You can check the further eligibility with the given below link.

https://engineering.careers360.com/articles/nata-eligibility-criteria

Good Luck!