In theory, you can do pre-med with any major, but the UCLA MSE major leaves essentially no free elective space to take the pre-med courses that are not already covered by the MSE major.
http://www.seasoasa.ucla.edu/curricular-requirements-department-information/
It seems difficult to find information on changing into the UCLA College of Letters and Science. Contact the division to find out more information.
It does not seem to be difficult to declare a biology major once you are in the College of Letters and Science:
https://www.eeb.ucla.edu/ugrad_declare.php
https://www.mcdb.ucla.edu/undergraduate/major-requirements