TL;DR Yes, energy can produce matter by colliding way too many photons together to produce matter-antimatter pairs.
The Mass-Energy Equivalence
The Mass-Energy equivalence suggests the mass of a stationary body has some internal or intrinsic energy, called its rest energy. For example, If you seal up a nuclear bomb and let it explode containing all the heat and products in a box, the box has the same total mass before and after the explosion. This is basically what Einstein proposed, and what E=MC squared implies. But is the reverse true?
Can energy be somehow converted into mass?
As we know that rest mass can be converted to energy by nuclear fusion and nuclear fission processes taking into account the binding energy and mass defect. But what about the other way round?
Can any arbitrary form/kind and amount of energy be used in this process? The answer to this question is no. Any arbitrary form of energy cannot be converted to any arbitrary type of mass (otherwise nuclei converters would use garbage as input!). For any type of energy to be converted to mass, a nuclear reaction is required that absorbs energy and releases a particle that has rest mass.
If an object gains energy it gains mass, and if an object gains mass it equivalently gains energy. This conversion deals with very small amounts of mass and significantly very large amounts of energy. The conversion also requires creation or destruction of particles that violates all the conservation laws.
How does all this even make sense? Try to grasp this first.
Now that we are somewhat familiar with the concept of mass-energy equivalence and its implications, we move forward to our original question.
How do we convert energy to rest mass?
Matter – Antimatter Pair Production
Pair production is the creation of an elementary particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specifically to a photon creating an electron-positron pair near a nucleus. In order for pair production to occur, the incoming energy of the interaction must be above a threshold in order to create the pair – at least the total rest mass energy of the two particles – and that the situation allows both energy and momentum to be conserved. (Source)
Now, a suggested way to bring about this conversion is by converting a pair of photons (particles of light) into an electron and its antiparticle – positron inside a subatomic particle collider. For this experiment to take place it first requires building of a new type of subatomic particle collider which is less complex than the one built in Europe (LHC).
The implementation of this idea is not void but is quite plausible with the existing forms of technology. All that is needed to be done is to accelerate electrons with a high-energy laser to a speed just below the speed of light. These high energy electrons are then shot into a slab of gold (target) creating a high energy photon beam (billion times more intense than the light from the sun). These photons generated are then aimed into a hollow gold shell/tube and fired through the middle of that specialized tube.
The tube is a special one. It is excited by another laser in order to create a thermal radiation field that emits light, whose brightness is similar to that of starlight. When light from these two sources crosses, some pairs of photons collide and create electrons and its antimatter particles, positrons. After the conversion of photon pairs into these two particles, a magnetic field separates the particles as they emerge from the end of the tube. This process has a lot of math behind it, see it here.
The Large Hadron Collider
The best example of conversion of energy into mass is seen in large collider experiments such as the LHC (Large Hadron Collider) in Europe. The original two protons that collide at the LHC create multiple protons and electrons (and their antiparticles) and this additional matter that is produced is produced from the kinetic energy of the original protons. The discovery of a new particle at LHC on 4 July 2012 was later confirmed to be the discovery of Higgs boson. It is said to be one of the most important discoveries in the field of particle physics theory as it is said to be an elementary particle in the Standard Model of particle physics.
For an insight you can click here or can see the following video.