I don't want to dwell on whether this justifies the existence of God. Rather, I'd like to point out that physics has largely answered this question, at least if it is reframed as "how" rather than "why".
A three-dimensional space can be geometrically open, closed or "flat", and my scientific career was launched largely by a quest to show whether the universe we inhabit is the last of these. At the time, that meant working out how much dark matter there is, because Einstein's theory of general relativity tells us that the universe's geometry depends on the mass and energy within it. We thought too little dark matter would produce an open universe, which would expand forever. Too much would give a closed universe, destined to collapse. A flat universe would be just between the two: its expansion would slow to a halt. Astronomers had yet to demonstrate that there was enough dark matter to stop the universe expanding forever, but we theorists were confident that our universe was flat.
Key to this was the notion of inflation, introduced by physicist Alan Guth to explain several cosmological puzzles, including that the universe appeared close to flat even after 14 billion years of expansion. A flat universe is like the top of a hill. If you are a little away from it - a bit open or a bit closed - the expansion of the universe soon drives you far away from this value, just as a ball that is a short distance from a hilltop will roll down to the bottom. Inflation, on the other hand, drives the universe towards flatness - just as blowing up a ball reduces the curvature of its surface.
But as Guth emphasised, there is another reason for favouring a flat universe: it is fundamentally beautiful. In a flat universe, the total gravitational energy is precisely zero.
A zero-energy universe may sound strange, but it relates to an idea taught in high school physics. A ball thrown up in the air has two forms of energy: kinetic and potential. If the sense of the kinetic energy is taken as positive, the potential energy, due to the gravitational pull of the Earth, is negative. If the positive portion of the energy beats the negative portion, the ball will escape from Earth. If the negative energy is greater, it will return. If the total energy is precisely zero the ball will barely escape - slowing to a stop when it is infinitely far away.
In terms of general relativity, the curvature of our expanding universe is related to the total gravitational energy of the objects being carried along with its expansion. In a flat universe, the total energy is zero. So a flat universe could have arisen from nothing. One can trade off the positive energy of particles for the negative energy of gravity and move from a situation in which there are no particles to one with a lot. As Guth put it: "There is such a thing as a free lunch!"
In recent years astronomers have discovered that we do seem to live in a flat universe, although we were wrong about how this comes about. Dark energy, not dark matter, appears to dominate, and it turns out that the strange nature of this stuff means that the geometry of the universe no longer determines its future.
We turned out to be wrong about how a flat universe comes about
The key point, however, is that with zero total energy, Aquinas's puzzle is resolvable. And once the energy fluctuations of quantum mechanics are thrown into the mix, the idea of something arising from nothing can become not just possible, but necessary.
Purists will argue that this begs the question of how the physical laws that make it all possible arose. Nevertheless, science has once again altered the playing field for such metaphysical speculations in a dramatic and beautiful way.