The question is if he would be able to obtain a parole, if he asks for it, when he enters the country so he could be able to have a work permit during that year.
Generally speaking, parole is granted to Cuban nationals who cannot be returned to Cuba. In this case, you are describing someone who can be removed to Canada. Parole is granted in the exercise of discretion and is not obtainable as a matter of right. Whether CBP would do so in this case most likely depends on a number of different factors that would need to be evaluated. Keep in mind that employment authorization is not immediately issued but takes a number of months to get, even when an alien is paroled in the public interest.
Thanks for your advised, do you think it will be better to enter US and wait for a year to apply for CAA?
This forum is not the place to get case specific advice. Consult with an experienced immigration attorney who can review the facts of the case and advise you how best to proceed.