Stephen Hawking tried to answer that question in his book "A Brief History of Time". His answer is based on the uncertainty principle:

$$\Delta E\Delta t\geq \frac{\hbar}{2}$$

If you take that the total variance of energy of the universe to be $\Delta E=0$, then, according to this principle, you can have $\Delta t\rightarrow\infty$ and then, the universe can exist for an indefinite amount of time. The stated fact is that the total amount of energy of the universe is exactly $0$. The reason is that matter has "positive" energy from it's mass ($E=mc^2$) which is exactly balanced by "negative" binding energy (electrons in an atoms, atoms in molecules, planet orbiting stars, stars clusters, galaxies, galaxies clusters, superclusters, etc.). Thus, the universe would have a total amount of energy equals to $0$.