The solution to the anthropic principle appears to lie in the very early Universe, moments after the Big Bang, the inflation era. Our old view of the Universe was one of newtonian expansion, at less than the speed of light.
However, now we know that, because of symmetry breaking at the GUT (Grand Unification Theory) unification point, space-time and matter separated and a tremendous amount of energy was released. This energy produced an overpressure that was applied not to the particles of matter, but to spacetime itself. Basically, the particles stood still as the space between them expanded at an exponential rate.
Our visible Universe, the part of the Big Bang within our horizon, is effectively a ‘bubble’ on the larger Universe. However, those other bubbles are not physically real since they are outside our horizon. We can only relate to them in an imaginary, theoretical sense. They are outside our horizon and we will never be able to communicate with those other bubble universes.
Inflation’s answer to the anthropic principle of any form is that many bubble universes were created from the Big Bang. Our Universe had the appropriate physical constants that lead to the evolution of intelligent life. However, that evolution was not determined or required. There may exist many other universes with similar conditions, but where the emergent property of life or intelligence did not develop.
Hopefully a complete Theory of Everything will resolve the ‘how’ questions on the origin of physical constants. But a complete physical theory may be lacking the answers to ‘why’ questions, which is one of the reasons that modern science is in a crisis phase of development, our ability to understand ‘how’ has outpaced our ability to answer if we ‘should’.