When honestly talking religion and reason and how being came into existence, all sides need to be careful, honest, accurate and satisfied with limited results.
The common sense of human knowledge can clearly see that some being or beings structured, organized and regulates the world or universe.
The people of religions must say yes to this. However, we must say that we believe that this being or beings is the God that communicates to us and that He/It/They care for us. We cannot prove that; we believe that.
Modern logic, science, common sense and reasoning must be careful and acknowledge the complexity of the cosmos and agree: some being or beings structured, organized and regulates it.
All sides must admit limits, hopes, and honestly acknowledge: a being or beings made all of this. We cannot prove It/They are the beings of religious worship.
Now, concerning the Jewish and Christian backgrounds, we can demonstrate God’s existence by being His loving agents. God is love and His existence can be demonstrated in loving actions.