"Der Mann hat einen Käse."

[dpatt711]

Why do I need to say The man has A cheese, and isn't einen plural?

[Germandy]

"einen" is never plural. Here it is the accusative form of "ein Käse" (a cheese).

[alicecirjan]

You cannot say "a cheese" in English. Cheese is a noun without singular form, thus "some cheese" would be the correct form in this case.