For TN, you merely need Cdn citizenship, so that is not a problem.
What is a problem is that, from your post, neither you education nor the position that you were offered qualify for any TN category.
The job is not a computer systems ananlyst job, so why would you thing that would be the category. Besides, you don't have a CSA-related degree, nor any CSA-related experience. Marketing is not a TN category.
Your best shot might be as a management consultant TN, but that required 5 years experience.
You simply are not qualified for a TN, and certainly not a TN for the job you described.