Generally, oil paintings are painted on canvas or panel that don’t require mounting behind glass. On the other hand, mats are made of paper and need to be behind glass to keep them from being damaged. Their purpose is not just to serve as a design element; they also serve to keep the glass away from the artwork.

If you want the look of a mat without requiring glass, you can use a liner, which is a separate frame, often covered in linen, that goes between the primary frame and the painting.

You can also get moulding that has a built in liner. You trade off choice and price, like always in framing.

Anyway, you can expect the addition of a liner to nearly double the cost of framing, and sometimes more.