How do I get a data science internship without experience?

Internships are usually meant for people without experience, are you sure you are looking at the right companies?

A true Data Scientist position is technically not an entry-level role. You either need a graduate degree or industry experience or data science certification. So, you may need a previous data analysis or software engineering internship on your resume before you can be seriously considered for data science internships.

For more details check this awesome blog How To Find A Data Science Internship In 2021