If the energy/matter that was contained in the singularity before the Big Bang had always existed, and if it’s true that energy/matter cannot be created or destroyed, then what explains its existence?
That's a very complicated question!
First, let's remember that Moses didn't bring the Law of Conservation of Energy down from Sinai on stone tablets -- it's something that we've observed to be true of the universe today, and which our theories use to make very accurate predictions. But this doesn't mean that it was always true, and particularly that it was true early enough in the Big Bang that our current theories don't apply. We know that our current theories fail during the Planck Era, for example.
Second, Noether's Theorem says that energy conservation exists because the Lagrangians of mass-energy are time-symmetric. Time symmetry is a very good symmetry today in regionals of space small compared with the entire universe, but there may well have been eras in which it wasn't.
In fact, there probably were such eras, just as time-symmetry is not a good symmetry even today at very large scales. (The universe is expanding, and on the face of it, this causes a non-conservation of energy.)
Thirdly, if you try to save the law of conservation of energy by calculating the total energy of the entire universe including the gravitational energy, one reasonable set of arguments (energy calculations in General Relativity can be very difficult, since gravitational energy tends to be non-local) yields a total energy of zero! The mass-energy in the universe is exactly balanced by the gravitational potential energy. If this is correct, the total energy has always been zero.
But this is all speculative! Remember, that real physics is an experimental science and if you can't test a theory it may be interesting, but it isn't physics.
The simplest answer might be that mass/energy have always existed. For field-based inflation, their past eternality is prohibited by the Borde-Guth-Vilenkin theorem, but, as that theorem only prohibits it in a universe that is expanding "on average", they appear compatible with some of the bouncing cosmologies developed more recently, of which the simplest that's compatible with CMB data may be Poplawski's entirely relativistic version (using the fermions of the Einstein-Cartan version of GR, which have spatial extent) of the "baby universe" scenario, in which the gravitational collapse of any large rotating star includes tidal effects which initially separate the particles and antiparticles of virtual pairs, that are subsequently blown outward by energy until then tied up in particulate spin, when the collapsing star's fermions lock up against each other at extremely high densities. The "parenting" universe (which is on vastly larger scales of space and time) is analogous to the 3-D skin of a basketball, and is causally separated by the inertia of its own continuing expansion, as it would've begun in an earlier (and larger-scaled) version of the same process. Poplawski feels this cosmology to require a prevalent direction of rotation, so it is falsifiable and consequently scientific, however marginal that prevalence may be. (My reading of physics notation is very limited, so I've relied on his English verbiage for some of the inferences I've made here.)