It would be wrong to say that the universe is made of "matter" on the one hand, and "energy" on the other, as if they were two distinct substances that can be converted into each other. The universe is made of matter (particles that have mass) and non-matter (particles that do not have mass), and both matter and non-matter have energy.
Energy is not a substance of its own, it's a property that systems (including systems made of matter) can have.
A photon can have a certain amount of energy. But a photon is not energy; a photon is a particle, or alternatively a disturbance in the electromagnetic field. A gas molecule can have kinetic energy. But the gas molecule is not "made of" energy. It's made of atoms.
Note that the energy a photon (or gas molecule) has depends on your own speed. The faster you are traveling towards the source of the photon, the more blueshifted the photon will be, and the more energy the photon will have from your frame. So the energy can't be a substance that the photon has a fixed amount of. Energy is only conserved with respect to a given inertial frame; if you change the frame, the kinetic energy of everything in the universe changes.
Matter has energy deriving from its rest mass. It always has this energy. You can change the matter into other forms; you can (in theory) turn the matter into photons, or turn the photons back into matter. But the matter had just as much energy as the photons have, which is to say, neither are energy, they just both have the property of energy.