Could a mixture be made up of only elements and no compounds?

Let's distinguish the difference between the three keywords in your question: mixture, element, and compound. An element would be any of the chemicals on the periodic table. An element exists usually as one atom in nature, but some elements have more stability as a diatomic molecule (diatomic means the element occurs most naturally when it is paired with one other atom of the same element). A compound is a chemical bond between two or more different atoms, making it a molecule. A mixture, however, is a mingling of either multiple elements or compounds within the same "container" that do not ever chemically combine.
Substances within a mixture can be physically separated from each other as they never react chemically with one another. A mixture can have a mix of elements and compounds, or just a combination of one or the other. So yes! A mixture can contain just elements if those elements are not chemically reactive to one another. Air is a great example of an elemental mixture as it contains nitrogen, oxygen, and argon (along with some other compounds).