They are both right, intelligent design and evolution. Evolution is intelligent design.
All the discrepancies and missing links, the accelerated rapid rate and change of paces throughout the evolutionary process at certain times, is due to where everything originated from in the first place, the cosmos, the brain of "God." The entire process of evolution and life/consciousness, the accelerated rate of knowledge the past two centuries, the rate of intelligence, where everything derives from, is from the cosmos. Always has been. For billions of years. Cambrian explosion, and everything else. The book of life, the book of genetics. The pure conscious aspect of "consciousness and life" is the entire bible. All different forms of energy/light and DNA are from an outpouring from the cosmos, from celestial bodies, in forms of energy, and DNA. Life/consciousness....Our brains, as well as everything else, animals, plants, aquatic life... Are receivers. Supernova 1987, Eta Carinae, meteors, stars, the sun, etc etc etc. It all sustains life and changes life as the process of conscious and physical evolution carry on.
Newton's laws and Einstein's relativity really do explain it perfectly, when it comes to all of this, our human bodies and brains are not exempt from these laws.
Conscious evolution and physical evolution go hand in hand. Evolution is intelligent design. That invisible undetectable force that holds everything together and allows us to experience life. Religions and everyone who speaks for religions just have no idea what ID and consciousness is and distort it all completely.
Science has already proven this many times in many different ways, indirectly and unaware of it. We can change a cell with just a baby tiny little bit of electricity... Imagine the change in cells (ourselves, in our brains, and all life forms) consciously and physically from the massive, endless outpouring of all sorts of subatomic particles, gases, energy, DNA, and light from the cosmos, celestial bodies. Our evolution of intelligence and knowledge derives from the same place.