Now the question becomes not what is the
origin of life but the origin of biological information. Where did the
information to build the first living organism come from?
Valid question, the problem is you think you already have the answer. My answer is that we don't know... yet, but we have developed a number of plausible theories almost none of which would necessarily contradict each other. Here is a link if you actually care to learn about the leading theories.
You see, a scientist can't just invoke God because something seems to have no other explanation. If they did that, then we would still be woefully ignorant about... everything in the natural world. So many things that have been attributed to being directly controlled by God (Or depending on the time and culture gods, demons, ghosts, tree spirits etc.) have been shown to have natural explanations. That will very probably be the case with this issue as well.
Now if you want to keep shoving God back into the gaps of scientific knowledge feel free to do so, but you should know that in that case, your God is nothing more than an ever receding front being pushed backward farther and farther every year, and it's gonna take a lot more than a vague appeal to incredulity to stop that.