No, that is NOT what random means. Sure, the word is often used by creationists as if it meant that, but they are wrong.
This is very simple. DNA formation, and evolution, are not random processes. Calculations of any odds based on randomness have no bearing on evolution or DNA.
Then what does "random" mean in your world?
As in a card trick, the most important one is not the person who randomly picks a card, but the One who arranged the cards in the first place.
With evolution, what seems uncontolled, without any intelligent design, has actually been very precisely controlled from the outset, by the Master Magician, who laid all the cards in place.
It could be that the true Creation moment, was actually the creation of Evolution itself, which is a guiding process, empowered by God to bring about every living thing, and their future modifications, from the moment of the Big Bang, onward through time.