With an undergraduate degree, there are some job possibilities, but not that many. Some students interested in human factors and engineering psychology finish their undergraduate degree, take some time off to gain real-world experience and then go back to school to earn an advanced degree.
Having an advanced degree is really important for a human factors and engineering psychology job. Of course, job opportunities at various organizations are typically greater with a PhD versus a Master's degree. Also, it is important to keep in mind that some human factors and engineering psychologists hold academic positions at colleges/universities and serve as trainers, facilitators, assessors, coaches and consultants.