Michigan admits to the engineering division, but the requirements to declare a major from there is not difficult.
https://advising.engin.umich.edu/declaring-or-changing-major/
Compare to Purdue:
https://engineering.purdue.edu/ENE/Academics/FirstYear/T2M
At the various UCs and CPSLO, the difficulty or not of changing major varies, and may depend on the destination major. Examples:
http://mae.ucdavis.edu/changing-majors/
http://www.seasoasa.ucla.edu/within-engineering/
http://changeofmajor.uci.edu/
http://www.ucsd.edu/catalog/curric/SOE.html
https://eadvise.calpoly.edu/majors/changing-majors-within-ceng/