A. If by "prove to me" you mean "persuade me to become a Christian" then the answer is "no, and yes". The answer is "no" if we are thinking about me having the power and resources in myself to change your heart beliefs and affections. Clearly I can't. God alone has the power to be able to change you. Only God can make you fall in love with God. Having God change your inmost person in every fundamental way is what Jesus called being "born again." He says, "Do not be amazed that I said to you, 'You must be born again.'" (John 3:7 NASB) On the other hand, the answer is "yes, I can persuade you" in the sense that God does use even sinful people like me to tell others what they need to know. Even so, I can only plant the seed of truth and water it- God must make it grow (1 Corinthians 3:6-7, NASB). God really is your only hope.
Now, if by "prove to me" you mean "set forth a logical argument which demonstrates that God exists" then the answer is again "no, and yes". No, I can't set forth one all-encompassing argument which will leave you with no intellectual gaps. Not in one conversation or forty. But what I can give you is individual photos of God's truth and reality; mental snapshots which, over time and with God's grace, will open your eyes to the reality of God. Perhaps, actually, one snapshot would do it for you- but it would be because of God's work on your mind and not the completeness of the picture. Don't get me wrong: I don't believe there are any gaps in the reality of God- He Is! But He is infinite, so we can't capture all of Him with even a super wide-angle lens.
I want to bring up two more things in relation to your question. The first is your apparent assumption that unless I prove it, you are not obligated to believe it. But that is simply not the case. The burden of proof is not with God or with those who speak for Him (Christians). That would be like a little boy telling his mom that unless she can show him the ocean right now then he has the right not to believe in the existence of the ocean. The child may think he has the right to disbelieve, but the ocean is at that very moment rising, falling, and crashing on the shores just twenty miles east of him. Dear friend, we are all like that child- let us not think that we are the standard of what can and can't be true. And let us not give up the search just because our knowledge and experience are so limited.
And that brings me to my last point, which answers the question: "Okay. who is the standard of what is true and real?" Let me be very specific. The answer is the Christian God. The only God that exists is the one Who is revealed in the blessed pages of the Old and New Testaments. Nothing less; no one less. So, I won't ask you why you don't believe in the God of the Muslims because the reality is that Allah does not exist. Nor will I be baffled that you don't believe in God as some mere impersonal force. And so forth- there are a thousand versions of "God" that I would not try to defend and set forth to you. There is only one true, real, omnipresent God, and to know about the real Standard of Truth you must know the content of the Bible's revelation of Him. What's more, to actually know Him with mind-blazing certitude, "You must be born again."
We must all, in the end, tremble with joy beneath the God Who affirmed to Job (and to us sceptics) that He alone is the Standard:
'Who is this that darkens counsel
By words without knowledge?
Now gird up your loins like a man,
And I will ask you, and you instruct Me!
Where were you when I laid the foundation of the earth?
Tell Me, if you have understanding,
Who set its measurements? Since you know.
Or who stretched the line on it?
On what were its bases sunk?
Or who laid the cornerstone,
When the morning stars sang together
And all the sons of God shouted for joy?'"
(Job 38:1-7, NASB)