The question is too big for words alone. We need to see and be touched by the answers, in order to cope with the magnitude of the concept. In other words, "it’s better felt than tell’t". Our problem is that we are locked into our tiny view of our universe (like bugs on a rock), and we don’t even know what questions to ask. We are trying to understand God in human terms with human means.
We have to believe that God wants to be known and gave us the means. Not just to sit around drinking coffee and intellectualize or rationalize about Him, but to relate to Him, and experience Him with all of our senses that He gave us to understand our universe.
The creator and sustainer of the universe has provided humankind with a revelation of Himself through 3 major sources: 1) The natural world 2) Through His Son, Jesus Christ (as seen in the Bible) and 3) through the life invading power of His Holy Spirit.
Actually, the Bible itself does not seek to prove the existence of God; it simply affirms His existence by declaring, "In the beginning God..." (Genesis. 1:1).
God has revealed Himself through the physical universe (Psalms 19:1 & Romans 1:19-20). By opening our eyes and observing this natural universe, we can discover positive indications of God's existence. To an open mind, creation reveals the results of a universal mind that developed a master plan and just did it! It makes horse sense to accept the idea that God is Creator of the universe when the alternative is to assume that our orderly universe came into existence by chance. Rather like attending the launching of an Ocean Liner, where some nut slips up to you with a pamphlet informing you that this great ship was the result of random selection and they merely found it floating in the harbor...get my drift?
The greatest revelation of God, however, is found in the Bible. This is the written record of individuals inspired by their revelations and experiences of God. Both the existence of God and the nature of God are revealed in and through the person of Jesus Christ who is the central topic of the whole Bible. Jesus said, "He that has seen me, has seen the Father" (John 14:9). To get to know the Jesus of the Bible (not some man or religion’s version), is to get to know His Father God.
Although we cannot (with our tiny brains) fully understand God, we can get to know Him through developing a personal relationship with Him by faith and studying what the Bible teaches about His nature, power and attributes.
God might best be described in terms of His attributes, that is, His inherent characteristics. Here is one; Jesus taught that "God is Spirit" (John 4:24). God has no atomic body, no physical or measurable form bound to the laws that govern us. Thus, God is invisible to us. (Which is just as well, since we would probably vaporize if we saw Him!) He became visible in human form in the person of Jesus Christ, but His essence is invisible.
God Himself Is Changeless. Though progression and change occur in His kingdom, He remains unchanged (Hebrews. 1:12). If He changed, He would not be perfect. We can know for sure that God will not be different from one time to another. He is consistent with who He says He is and can’t be blamed for things outside of His nature. When you get to know Him you don’t ask all those dumb questions, like "why are people suffering?" etc.
God is all powerful; His power is unlimited. He can do anything provided it is consistent with His nature, character, and purpose (Genesis 17:1 & 18:14).
God is all knowing and possesses all knowledge (Job 38:39 & Romans. 11:33-36). Because God is everywhere at one and the same time, He knows everything simultaneously. Neat trick huh? He also has the power to know the thoughts and motives of every heart (Job 37:16, Psalm 147:5 & Hebrews 3:13). God Is Eternal. In relation to time, God sees past, present, and future. (2 Peter. 3:8 & Revelation. 1:8). Time is like a parade that we sees only for a segment during our lifetime. But God sees time in its entirety as though watching all of history on TV monitors. Imagine watching over His shoulder!
God Is Holy. The word holy means "to separate" and refers to God as apart from or exalted above other things (Isaiah. 6:1-3). Holiness also refers to God's moral excellence. Since He is holy, God requires holiness in His own children. And what He requires, He supplies as a free gift that we receive by faith through His Son, Jesus Christ (Ephesians. 4:24).
God is righteous. He knows right from wrong. When we come to know Him for who He is, we begin to share the same perspective and attitudes toward life.
God is love. This love is the essential, self-giving nature of God. God's love for us is designed to awaken our responsive love for him. God loved and gave; proving His love by giving His only Son on the cross for the redemption of humanity. God, in His love, wills good for all His creatures (Genesis. 1:31, Psalm 145:9 & Mark 10:18).
Also God is truth and God is wisdom and He is much more than we can write here. It remains for every human to find and prove these things for themselves or die in ignorance to face the consequences of apathy. But you read this far, so you are different!
We can know him through His Holy Spirit as well; All who give him back their lives as the last positive act of their own will, are promised the full resources of God’s Spirit. He invades our lives to enable supernatural expressions and proofs of God’s love to work through us. Read about it from Acts chapter 2 on.
Finally, if you are still looking for that succinct definition of "Who is God?" ....He is the one who has always loved you despite yourself.