I had an internship while in college with a company and they hired me right out of college. My son, also a mechanical engineer, had an internship while in college and that same company hired him right after graduation 4 years ago.
So, it is key to have relative experience by the time you graduation in a job field, industry, or company you want to enter. Keep in mind relative experience is not always via an 'internship' ... strong grades, relative experience (machinist, mechanic, robotics, automotive, or industry related), and attitude sometimes trumps 'formal' internships. However, if a company you are interested in does have internships, then their internship is generally the best way in.
I hope this helps. Best of luck!