The UCSD site says that one must be a student of UCSD for a year before being allowed into its college of engineering. The transfer page also says that a transfer is only a student of UCSD his first year, not one of the actual engineering college. Does this mean that it will take more than two years to graduate after transferring to UCSD as a mechanical engineering major?
I think you’re confusing being admitted directly into the major and having to apply to get into the major as a continuing student.
Mechanical engineering is an impacted major. A certain number of incoming freshmen and transfer students will be admitted into the major. Once it’s full, the remaining students will be admitted to UCSD but not to the mechanical engineering major (they may be admitted to their second choice major or as undeclared/undecided). Continuing students who wish to switch into mechanical engineering have to apply to get in and this is what happens when applications open up spring quarter. You only have to wait to apply to enter the major if you were not admitted to the major initially (when you are admitted to UCSD). Some students will be admitted directly into the major.
If you are admitted as undeclared, you can apply to enter the major as a continuing student and during that time that you are waiting you can still be taking the courses you need to apply to enter the major and to graduate in that major. However, according to this http://maeweb.ucsd.edu/sites/mae.ucsd.edu/files/FAQs%20MAE%20Impaction.pdf it may take you longer to graduate as a mechanical engineering major as a transfer student regardless of whether you are directly admitted into the major or enter as a continuing student. You can look at the course requirements for the major and map out yourself how long it will take you to graduate.