Before I believed in evolution, I would simply say that all vestigial characteristics (features and ‘junk genes’) were actually not vestigial at all and eventually science would uncover a function for all of them, as it seemed to have been doing. For example, a 2007 paper has apparently demonstrated a modern function and use for the appendix, besides other minor functions like holding tendons. When it came to the idea of junk DNA, I looked admirably to the project of ENCODE which said that 80% of genes had been shown to have a function, with 100% visible in the future. There has been much rejection of ENCODE’S results because of how they defined ‘function’ I think in their experiment. Nevertheless, I saw almost every day more papers getting published on function in some part of the genes not known before, so I was pretty happy about how things were going.
This all slowly came crashing down with my discovery of the vitellogenin gene which plays a major role for the egg yolk of the eggs birds lay. Apparently, by studying the position of this gene in birds, scientists were perfectly able to predict its locus in modern day humans, where it no longer plays any role in the formation of eggs in us (since we don’t lay eggs) and is therefore functionless. Ironically, all this was introduced to me via an article by the Institute of Creation Research providing information that ‘debunked’ the claim that vitellogenin was junk DNA, which at the time I read it convinced me.
Until in a debate on evolution with someone I was having, where someone brought it up and I responded by pointing to the ICR article, someone pointed me to this series by Biologos by @DennisVenema responding to ICR’s claims. I read all 5 posts, and it became undeniable to me: ICR was absolutely wrong. And thus was the first step of my transition to EC.
EDIT: A funny story: before I believed in evolution, I explained the vestigial ‘legs’ in snakes by saying that this actually proves the Genesis creation account, since Genesis says that the snake was punished for deceiving adam by flopping on its belly, which I took to mean God removed the snakes of the leg and therefore the vestigial features of snakes were clear proof of Genesis.