You do not need a job offer from Canada in order to be able to immigrate.
You can either become a PR (permanent resident) - then check EE (express entry) section of this forum and PNP (provincial nominee) section
Or you can go for studies (get accepted to a college or university in Canada) and get student visa (of course this type of immigration is a temporary one)
Or you can get an open work permit (there are some programs - like Working holiday in Canada) that allows you to do so.
Your reputable school does not really matter much to the local employers. They just do not touch anybody who needs visa and complicated LMIA on the top. At least most of them.
Check also if you fall under one of the Nafta agreed specialisation (that would give you possibility to avoid LMIA). And then be pro-active when it comes to contacting potential employers (they have lot of emails from all over the world, so your application is not really visible for them - especially if they omit anybody outside Canada).