Evolution (and, for that matter, practically any other physical process) involves some aspects that can be described as random and some that can’t. But we need to define “random”. Both those promoting randomness and those objecting often confuse different senses. “Random” can mean a specific mathematical pattern where something is best described (from a human perspective) by a probability. For example, flipping a coin, casting lots, will this particular atom decay in the next year, will a particular mutation occur. It can also mean something that is humanly unpredictable, but not probabilistic in that sense. For example, mathematically chaotic behavior has a precise outcome for any given input value, not a range of probabilities. But the outcome is so sensitive to the input value that it is practically unpredictable in the long term. Long-term weather is an example. Another category of unpredictable outcomes would be things that have no math formula, such as the long-term course of history (human history or earth history). Yet another sense of “random” is “unguided” or “purposeless”. But at what level? I can have a purpose for flipping a coin, but no amount of study of the coin or the laws of physics governing it will detect my purpose for it.
All of the above categories include things that the Bible affirms are under God’s control. All of them can apply to certain aspects of evolution, though there are significantly non-random aspects as well. The laws of nature provide significant constraints on what can evolve, for example. The laws of nature have no goals of their own that could be found by studying them; they are merely patterns and means used by God, as Genesis 1 points out. We have to look to God to discern the purpose. The randomness in evolution seems to be a good way to create diversity; perhaps that is a reason to use it as a method of creation.