Peace,
Science can co-exist with religion, one does not exclude the other. God and His religion is difficult or even impossible to explain using science, but you can explain science with religion when thinking about creation. Religion does not have many rules of thumb except what is written in God's scripture and you can not verify it by conventional means.
Well, religion and science are not compatible. Science exists because God created a functional world so mankind can explain how it works in their primitive or limited ways. God and His religion is the root which everything originates from, including science. You can explain it like in an operating system access restriction, the root needs Super User (SU) access and the standard user (the human) has no read/write/view access to the root. The SU (God) can execute commands which are visible (regarded as signs) to humans in the operating system (game world) which is the source of Guidance in this world. The root environment is what is regarded as Unseen in Quran.
Since science or mankind has no root access it is unable to find any traces of God which its methods can discover. We can only find God by abstract thinking and spirituality. This is why religion is completely incompatible with science as it needs access to root to research.
God bless you