No/yes, and no
Does all matter exist forever?
No, because matter can become energy, in accordance with Einstein's famous formula E=mc2.
Nuclear power demonstrates this. If you weigh the fuel as it goes into the reactor, and then weigh the fuel and all of its waste products as it comes out again, the used fuel and the waste weighs less than the unused fuel. The difference in mass is the energy that has been released.
Another example is annihilation. When an antiparticle meets a particle, they are destroyed and their mass becomes energy.
So no, mass does not need to exist forever.
But if we then modify the question:
Does all mass and energy exist forever?
Yes it does, in an isolated system.
The question is if we can consider our universe an "isolated system", since it is constantly expanding, but it is rather safe to say that mass and energy cannot be destroyed.
Does that mean we exist forever?
No, it does not. Our mass and energy may always exist, but in the end they will be useless. Because every spontaneous action increases entropy.
Entropy may be a difficult concept to understand but put very simplistically: entropy is a measure of how much waste energy there is. Energy is considered "waste" when it cannot do any useful work.
By contrast, energy that can do useful work is called exergy.
We humans need exergy to function. The physical processes that drive our bodies and our minds require exergy. Without exergy, we cannot exist. We would just be lifeless matter, completely lifeless even down on a very basic physical level in that we could not even affect any kind of chemical or nuclear reaction to happen.
And this is what eventually will happen. It is one of the basic laws of physics that — in an isolated system — the amount of exergy can only decrease, and the amount of entropy can only increase. This process cannot be reversed. In the end, all exergy will be spent, and only entropy remains. This this state is called the heat death of the universe.
And when we reach that state, we will be no more.