Can young people get colorectal cancer? If there is no family history and if the person is under 30, should they be concerned about getting colorectal cancer?

In short, yes but. It is much less often than in folks over the age of 45. Young folks with colitis or a family history of colon polyps or cancer are at increased risk. If you are having symptoms related to your colon that are persistent, see a GI doctor or colorectal surgeon and let them decide if diagnostic testing is necessary.
Yes, but it is rare. Colon cancer is rare under age 40. It can occur in people with predisposing conditions like ulcerative colitis or familial polyposis. The vast majority of cases occur in people over 50. That is the age when screeing should start for most people. In short, colon cancer should be low on the list of concerns for someone in their 20s (unless they have the conditions i mention above).