Suppose the universe contained only low-mass stars. Would elements heavier than carbon exist?

No, since they don't have the necessary mass and a high temperature in their core.

Explanation:

There are two forces that play an important role in the stars: the force of gravity in the inward direction due to stars' own mass and the radiation pressure in the upward direction as a consequence of the nuclear reaction in their core.

The superficial layers of the stars compress the core as an effect of their own gravity. Therefore, atoms will be closer to each other in the core, allowing them to combine, increasing the density and temperature.

A nuclear reaction occurs when light elements combine into heavier elements (that is known as nucleosynthesis). To get fusion reactions that generate heavier elements than carbon high temperature is necessary, which can be gotten by a more massive star for what was already explained in the first paragraph.