Sure, yeah it is not impossible because facts and logic can be employed to come to any number of conclusions.
It is important to point out that we are not creatures of pure reason. There are numerous other factors and faculties that inform the conclusions we come to and the logic we accept.
In other words, there are plenty of logical arguments that can be made and have been made for the existence and lordship of the God of the Bible, but in our sin and in our pomp we also can employ our God-given powers of reason to draw our own, incorrect, conclusions that no such God exists.
Just because something may seem logical to us doesn't mean it is true. Truth is the real heart of the matter.