I have a number of positions that I accept based on the evidence regarding that position.
When I learned insect systematics, the group Streptsiptera was taught as a family in the order Coleoptera. It has since been elevated to order status and I have watched entire lectures on the evidence supporting that hypothesis. Based on that evidence I accept the hypothesis, but I doubt that is what you mean here. I could look up some of the evidence I have reviewed on that subject if you would be interested.
Regarding the global flood story depicted in the Book of Genesis, I do not accept it as a description of an actual event based on the available evidence.
For one, there is no universal genetic bottleneck that should exist given the conditions of the story. There is no global geological layer that should exist based on the parameters of the story. Polystrate fossils were explained 135 years ago and I consider that explanation valid today as well, so they are not evidence of a global flood. There exist haplotypes in the human population that should not exist if there was a global flood. There is no evidence of discontinuity in many cultures that existed at the alleged time of the flood. Flood myths are not universal and do not exist in every culture. Some cultures have flood myths that are not at all about global flooding. I see no reason to consider the story in Genesis to be anything more than allegory and belief in God is not impacted for me as a result.
Regarding the theory of evolution, it is actually three theories. Common descent, change over time and the mechanism of natural selection. All of these have large bodies of evidence supporting them. In the cases of common descent and change over time, there are different evidences from fields of geology, paleontology, genetics, molecular biology, morphology, physiology, cytogenetics, biochemistry, chemistry and physics as well as other fields of science.
I would have to look for the reference, but a recent study on natural selection was able to demonstrate it in action. Speciation and even the evolution of genera have been observed or demonstrated in very recent times. Based on geological evidence of core samples, Lake Victoria in Africa has been determined to be about 15,000 years old and was formerly a stream that was impounded. Among the species that were in that stream was a founder population of cichlid fish that evolved in a very short time into nearly 700 different species and a number of different genera that compose part of the lake fauna today. This superflock is largely endemic and species are found no where else in the world. This is evidence for evolution and, it turns out, against a global flood, since there is no reasonable mechanism for a flood that would selectively place a group of fresh water species in a specific body of fresh water and no other.
How about lactase persistence? There is a lot of evidence for the evolution of that trait and even evidence that I accept indicating that the evolution of the trait in different populations was convergent. There are different mutations for the phenotype.