I'm a non-CS new grad in STEM with this exact situation. do you suggest a no-name internship, studying algorithms, or both?
Studying algorithms is HUGELY IMPORTANT. They say they "just want to see how you think." That's a lie. Big Tech interviews are like a whiteboarding final exam, and you need to shoot for an A.
Study leetcode. Study resources like interviewcake.com or Cracking the Coding Interview, and take practice interviews at interviewing.io.
Good luck, and feel free to hit me up for advice.