As a follow up this may be of interest. It explains the mathematical mechanism of evolution.
Environment: “If certain conditions are present”
View: https://www.youtube.com/watch?v=N3tRFayqVtk
The principles of evolution can be clearly observed even over relatively short timespans. Everything from dog breeding and strawberry cultivation to NFL linemen are all examples of the principles of evolution, where conscious human selection augments natural selection and accelerates the impacts of evolution over relatively short timeframes.
The trouble I think people often have, comes with extrapolating the effects over relatively long periods of time. Some people simply don't believe the Earth has been around long enough for large-scale evolution. Or perhaps some can't wrap their brain around evolution on a scale of billions of years (if you reduce evolution to a statement such as "humans evolved from single-celled organisms" or "humans evolved from apes" it is easier for some to reject out of hand, especially when using the relatively short human lifespan as a point of reference). Or the idea that human beings have evolved from single-cellular organisms is upsetting, because people feel like that somehow makes human beings less special (which I have never really understood. If anything the process of evolution over billions of relative years makes humans more special, not less).
It is important to understand how things are connected.
For example, you can't accept on the one hand that DNA is a valid form of forensic evidence, and on the other hand reject the theory of evolution. One thing follows from the other. Either our cells are constructed beginning at conception using instructions from our DNA (in which case evolution is a valid theory) or they aren't. I find that people are often willing to accept the validity of DNA science without question, because it serves an important function, and they don't see it as something that challenges their assumptions. The same people often reject the theory evolution out of hand, because they see it as something that directly contradicts their fundamental assumptions.
In any case, the theory of Evolution wouldn't "explain all the mysteries of life and the Universe". Evolution is a logical extension of physics, but it does not purport to be a "theory of everything" (which is not a matter of theology or religion anyhow. A theory of everything can be related to theology without being theological in nature. In other words, a scientific theory of everything may find itself compatible with a theological framework. This is not something to be afraid of). Evolution is more of a scientific framework for understanding life in the context of Earth. It is true that in order to comprehensively evaluate the nature of life on Earth, one would have to comprehensively evaluate the entire Universe.
The Universe proceeds from an infinite precession of physics (a point being an imaginary object, and a "point of infinite density" being a misnomer. The Singularity is a unified phenomenon; the physics of the present, proceeding ad infinitum relative to an infinite precession of physics).
The entire infinite precession from which the Universe proceeds is directly relevant to the formation of our Solar System. Our Solar System is the effect of infinite cause. Therefore even if human life as we know it originated on Earth, human life as we know it can be accurately described as the effect of infinite cause that we call the present, without contradicting Darwin's theory of evolution.