This topic is dealt in an extensive way in the philosophical texts like Shiva gnana bodham. Here the topic is discussed in brief.
If we take anything in the world there is something behind it for it to get created. If there is a stool there would be a carpenter behind it, a space craft - there would be a lots of scientists and technicians behind it and so on. This big Universe that exists also should have been made by something. It could be argued that this came into existence because of the transformation of something else that existed before. But how did that come from? If we trace the path there should be ultimately something that is the reason behind all these things. That one which was the cause of all these things to come into existence is what we call as God.
So what is great about it? If we carefully look all the things we call as made are actually transformed from one form to other. So only the transformation takes place but no creation. But initially all these things or their predecessors were created by something we call God. So it is this God we can really call the source. All other things we call sources in the day to day life are just transformers in truth. This power that created these things should be extremely powerful to be a real source! So It deserves our salutations.
Without creation how come all these worlds come into existence? If not so, by what means are the worlds created ? The ignorant raise many doubt about your existence.
This is one logical reply for the people who need proof to believe anything. The proofs are required only when a truth is not perceived. Who asks for proof for the existence of the air even when nobody physically sees it? When one can experience that Supreme in the self what other proof is required. It could still be asked that this experience could be an illusion. But it can be boldly said NO. The proof for it? Now we are talking about experience. This is something to be felt, not to be talked or proved. It cannot be done, unless the other party is trying to experience it. Otherwise it would be like telling about romance to a child, which is not grown to experience that feeling.
But that way one can always say all the illusions to be real experience. No, when these experiences are analyzed, it is very easy distinguish in neutrality which is an illusion and which is reality. The experience of God is not something as normal as any other feeling. It is something that is great that corrects us, liberates us, puts us in eternal bliss. Something beyond the reach of words, the greatness in silence. Hail that Absolute.
1. Concept of God in Hinduism