Most people don't know that there is a difference between the observation of evolution and the theory of evolution. The theory as set forth by Darwin shows the science of evolution which is undisputable fact, but goes further to say that the mechanism that drives evolution is random chance mutations, which negates the possibility of God. I believe that God designed life to evolve based on His evolutionary guidelines. Scientist have learned that environment and available food sources triggers specific DNA codes to cause dormant DNA sequences to become active and adapt that life form to it's environment.
So, yes, the Neanderthals were as much of God's creation as we are. Some interbreeding occurred with the Neanderthals and in such some of their DNA is still present in modern humans, but all true Neanderthals were killed off by what we know as modern day humans.
Recently, the DNA of snakes was decoded and scientist found that the snakes have all the DNA required to make legs, but the trigger to activate leg growth is turned off. I suspect that in the coming years, as more and more life form's DNA are decoded, we will find that from the earliest ameba, the DNA for all life forms was included in the first single cell organisms. Survival of the fittest and natural selection are real driving forces in evolution, but there are no random chance mutations that turned fish into frogs or eventually apes and humans. Scientist used to call most of the DNA in any cell, "junk" DNA because they didn't believe that it was being used. They are now discovering that it is not Junk, but dormant DNA waiting to be activated to cause evolutionary changes when survival requires it.
Evolution is designed by God and it is written in the DNA of all living things to ensure survival and to progress the life to a higher and more complex form.