Welcome to EvC. And you are not alone in losing your religious beliefs. I arrived at EvC five years ago as an evangelical Christian, and had been one for 20+ years, and I am now essentially agnostic atheist for most purposes. Many others here are in a similart position so you are among like-minded individuals
Your depiction of evolution seems to contain only part of the story - that of random mutation. Yes, random mutation creates noise - that is the whole point. It is the random number generator of a Monte-Carlo simulation. Evolution is driven by imperfect reproduction operated on by the filter of natural selection. Random mutation creates the myriad of possible changes between generations, and natural selection filters these changes, weeding out those that are sufficiently detrimental to future reproductive success. It really is that simple.
Have a look at this video to see how the process of evolution could begin, operating on nothing but random strings of polymers. It's worth diving in to 2min 40 secs on first viewing...