$E=mc^2$ this is the equation by Einstein claiming energy can change from energy to mass. this would happened at the big bang I assume, when electrons and protons were made to create hydrogen and some helium.
The law of conservation of energy states that the amount of energy doesn't change.
This is basically a definition of energy. That is, if according to your current definition of energy, there is some disappearing or appearing , that means your definition is not complete enough.
Einstein equation $E=mc^2$ means that mass is a form of energy. It's not energy changing into mass, it's a given form of energy changing in another form that is mass.
It can be observed when two particles with high velocity collides. Particles are created during collision, whose mass includes the former kinetic energy.
The equation $E =mc^2$ describes the mass–energy equivalence in relativity. It indicates that mass and energy are indeed the same thing, they are convertible.
One way to convert matter into usable energy is to annihilate matter with antimatter. And the energy released is proportional to the mass as the equation $E =mc^2$ shows, which means it is very efficient.
The common but less efficient ways to convert matter into energy are nuclear fusion and nuclear fission.
Nuclear fusion is a type of nuclear reaction. It is the process of colliding two or more atomic nuclei at very high speed and joining them to form a new type of atomic nucleus. The first man-made nuclear fusion on a large scale was carried out on November 1, 1952, in the Ivy Mike hydrogen bomb test.
Sun generates its energy through a fusion process called proton–proton chain reaction, which converts hydrogen to helium at a very high temperature.
Nuclear fission is the process in which the nucleus of an atom is split into smaller parts. It can be either a nuclear reaction or a radioactive decay process. It is commonly used in nuclear power plant to produce nuclear power.
You can read more about the mass–energy equivalence here if you like.