For engineering, there is a specific program that allows incoming first-years to take specific courses.
For other faculties, no, you cannot - you are not considered a student until September, so you can't register for courses now. Also, for second term summer school, courses begin on June 22, when you're not even done high school, and most (though not all) of the second-term courses have first-term prereqs. This is why there is a special program for incoming first-years in engineering - the timing wouldn't work otherwise.
Lastly, a course in summer school is different from during the year and probably isn't the best introduction to university. Things move very quickly, so you won't have much time to figure stuff out.
Literally thousands of people have full course loads in first year and do just fine, so unless you have a specific reason why you feel like you can't handle it, don't be scared by the prospect of a full course load. If you find you're having trouble once you've started, you can always drop some courses and take them in the summer after first year.
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