As per Scylla's remark, the best way to get a job if you require sponsorship is to apply directly. However. This is not a case of firing off your resume to every company - you will need to either be specialist (and therefore have skills that are in demand or work in a small industry) or you will need to be very well networked. Another way is to get an internal transfer with your current company (assuming they have a location in Canada).
This is coming from someone who worked in a niche market as a corporate recruiter and was offered a job to move to a competitor in Canada.
Most companies won't pay a recruitment agency fee for an LMO candidate unless it's a retained international search and the company knows they have to bring in international talent. That work is quite niche so the high street agencies (Randstaad, Adecco etc) will unlikely take this kind of work on.
My advice? Look realistically at your options - if you can come over here on your own means then do it - whether it be study, working holiday visa etc etc. If those aren't options, work out how to market yourself to companies using your network.
Hope this helps