I can't tell you why you SHOULD believe in God. I can tell you why I believe in God. Evaluate it as you will.
To me it's utterly illogical for there NOT to be a God--"stuff" doesn't just happen at random--that goes against all science. God need not have a "beginning" or a creator because that is the same as kids who want to argue with you when you try to explain math to them. "OK, but infinity plus one billion is LARGER than infinity" they will say, making it abundantly clear that they do NOT grasp the concept of infinity. Infinity can not be subjected to multiplication, division, addition, or subtraction. It's like that with the concept of God.
To say there is a creator, however, doesn't describe the God I'm referring to. God is PERSONAL, not a watchmaker, not a lame name for the universe. I am talking about the God of the Bible. If we look at the believers, such as Abraham, Moses, and Solomon, there is no evidence any of them were insane or delusional, yet they each tell us some important things about God. Abraham was a man of wealth and he trusted that God did speak with him and made him promises that seemed to be senseless (remember Abraham was old and childless, yet he is to be the father of nations). He left his own land and took his people because God told him to and amazing things happened when he acted on this faith. If he were just a psychotic or schizophrenic who heard voices, this outcome simply would not have happened--we've got a surfeit of mentally ill people and it doesn't turn out well for them. Thing after thing that Abraham listened to God about came to pass.
Moses had no need to stop being prince of Egypt. Civil wars and coups are common throughout history. How did he survive that time in the desert? Why would a stuttering "Egyptian" unfamiliar with the Hebrew religion be able to lead a people? Why when he finally complained to God that he couldn't take the burden anymore did God divide Moses responsibility among 70 men to do the job one had been doing?
Solomon is reputed to be the wisest man of all time. Why would a king "bow down" to another power? After all, we saw Egyptians, Greeks, Romans, and others just tell the people THEY were divine and for the most part, who was going to quarrel with the king over that claim?
Jesus came in fulfillment of the Scriptures. Scriptures written long before He arrived. He performed numerous miracles--including tricky ones like raising from the dead--the most impressive one being Lazarus who had been buried long enough that the burial process should have done him in if he hadn't been dead to begin with. His death is indisputable. His resurrected body was seen by too many over too long a period of time to be "mass hallucinations" at work. More to the point, He caused a group of people to change their lives COMPLETELY and live hard lives preaching an unpopular position which brought them a lot of hatred, NO wealth, NO power, NO prestige, NO casual sex, NO anything that tends to motivate people. Even on pain of death they would NOT renounce the Lord and there was NOTHING in it for them that can be explained away by psychiatric disorders or secondary gain.
Millions have personal experience with God. Sorry, they're not all nuts no matter what kind of casual insults get tossed about. Silly people claim that being religious removes personal responsibility, etc. These people should know of what they speak BEFORE they reveal their ignorance. Both Judaism and Christianity hold the individual TOTALLY responsible for his actions and promise an ETERNAL judgement. It's irrelevant if an atheist doesn't believe in it, the person believes and if he believes he shall have an eternal judgement THAT is the logical standard by which to evaluate his sincerity.
The fact that God remains mysterious to us, we haven't "figured Him out" doesn't mean diddly. If we used that standard then no one would take an aspirin (it's mechanism of action is not fully understood from what I've read--many theories, but it's rather a "miracle drug"), bumble bees would NOT be acknowleged to fly (we didn't "get" it for a LONG time, but at what point should you "give up" because it doesn't fit with existing knowledge?), and physicists would stop searching for the TOE (Theory of Everything aka GUT--Grand Unified Theory).
No one has yet to come up with a satisfactory explanation of why a sunset is beautiful--it does NOT have to be. In fact, "beauty" need NOT exist. There is no scientific need for the concept or the experience.
The existence of God and what He told us through the Bible explains a great deal about human nature and about the world in which we live. Both Jewish and Christian religions are responsible for a vast amount of knowledge and its preservation over the centuries when others have attempted to stamp it all out.
The vast majority of the major scientists throughout history were believers. It's really a post-WWII phenomenon that became fashionable among "scientists" (some may have a degree but they really don't make the cut--they're not remotely logical and have emotional attachments to unprovable theories but scream "it's science" just like a 2-year-old screams "it's MINE!") to scream "there is no God." There is nothing within science which can disprove or prove the existence of God. It's not constructed for that purpose. Science can also NEVER tell us that blue is the "prettiest" color and it's irrelevant that at least in the US most people probably think it's their favorite color.
It's rather like people who prattle on about "statistics prove" something. Statistics can not PROVE in the scientific sense anything. Statistics merely provide a confidence level at which we have reason to believe that something didn't happen randomly if inferential or they merely describe if descriptive. They don't "prove" diddly and when I hear people make that claim I know they don't understand statistics, so I have to consider that fact when they go on about their "argument" which can't rely on such "proof."
So, no, I can't "prove" the existence of God, but I have reasons why I believe in God, including the logical one that "stuff" doesn't just happen for no cause. If someone wants to think they've "got me" by saying, "so who created God," then I know I have someone who is like a child who wants to perform mathematical operations on a concept he does not grasp--infinity. God's existence is not subject to an opinion poll. Information is presented and people accept or reject for their own reasons and they will choose the consequences. God gave man free will and as He allows people to reject Him, there's nothing much the rest of us can do other than provide our reasons for belief.