A Canadian citizen with a complete packet can apply at a port of entry without an advance petition, so the calendar is governed by how quickly the agency and consultancy produce correct letters, not by a government queue. A USCIS I-129 filing takes longer and is optional.
Fix the structure first, because it cannot be fixed in the inspection lane
The fastest path for a Canadian is direct application at a port of entry or preclearance point with the employer letter, credential and proof of citizenship. That path has no waiting period, but it also has no appeal: a refusal on a structural point sends the applicant home to fix the letter and try again. For a case with a staffing-agency wrinkle, the time worth spending is on the two letters, the services agreement and the decision about employee status, which usually takes a week or two of back-and-forth.
The alternative of having the agency file Form I-129 with USCIS lets the paper be reviewed before travel and, with premium processing where available, produces a decision on a known timeline, at additional fee. Whichever path is chosen, the applicant should not begin remote work for the consultancy from Alberta on the assumption that admission is a formality, and should not travel on a visitor basis to start early.