A Canadian citizen can apply at a port of entry on the day of travel, so the constraint is having a correct letter and credentials ready. Ten days is feasible if the agency cooperates immediately; an I-129 petition would not be.
Fast is possible only with a finished letter
Hypothetical example: a Rothesay CPA is told the manufacturing client's reporting deadline requires her on site within ten days. The port-of-entry route makes that possible in principle, because there is no petition to wait for, but only if the agency produces a letter that names the client, the project, the dates, the salary and the accounting duties, and if she has her CPA certificate and passport in hand. The most common cause of a refused or delayed application under time pressure is a letter drafted by the agency's recruiting team that describes staffing rather than a professional engagement.
She should ask the agency to send the draft letter for review within two days, obtain her letter of good standing from the provincial CPA body immediately and plan the crossing for a day that allows a second attempt if the officer asks for something more. The client should be told the start date is subject to admission.