if someone says "it can not exist because science has not found evidence for it" they are actually incorrect, because something can exist but not be detectable for science.
Yes, but we should distinguish between that which is contingently undetectable, and that which is undetectable in principle (necessarily undetectable). The former is just waiting for the right detector to be in the right place. Those things exist whether discovered yet or not. The latter can be said to be indistinguishable from the non-existent, since they cannot impact on experience, and can be treated as such. To claim that things exist that are causally disconnected from our reality is a meaningless metaphysical statement - not correct and not (even) wrong.
Incidentally, the word science, if it is used to mean the formal study of nature in controlled settings like laboratories and observatories, is far too limited a concept for how we decide what is true about the world. Empiricism is a better term, since it includes the learning that results from every day personal experience. Most of my useful knowledge comes from that, knowledge like where to go for good Italian food, how to get there, and what kind of experience to expect there based on prior experience there.
My knowledge that comes from science isn't really very useful except as stimulation. I love to watch the shows like How The Universe Works, and I do learn a lot from them, but it's not directly useful information in my life.
science has not yet discovered the realm of God
This is where the distinction above comes into play. Is this realm necessarily or contingently undetectable? If the former, you will never detect it because functionally, it doesn't exist.
What is definition of existing?
Good question. My answer is that to be said to exist is to be said to occupy space and time and to be able to interact with other objects and processes that exist,like a wolf. To exist is to be real (synonymous), and reality is the collection of existent things. To be nonexistent is to lack all of that, like a werewolf.
So until science discover it, it does not exist?
Did you mean discovered by the senses? Either way, no.
one has to look at religious belief and science as two different aspects of life
I'd generalize that further. I've already explained why I prefer the larger category of empiricism to science, or the means of acquiring evidence-based beliefs about reality. I would expand religious belief to include all faith-based belief. These two are justified and unjustified belief, and these are two different paths to belief. Only one is capable of generating demonstrably true statements about reality.