The first point we need to make is that to establish the God of the bible as being the true God, we need to establish the bible as truth. The bible clearly declared who God is and that he is the only true God, but can we trust the bible?
What makes the bible true?
The only point needed in this question is that the bible is God's word, and he doesn't lie (Therefore we can trust the bible). But alas, that wouldn't satisfy me if I wasn't a Christian - even if it was the truth. So here are some other things to consider.
- Historical Evidence
How do we know the bible isn't just made up? Well there are a number of reasons for this. Historically it fits quite perfectly with everything else we know about the world and if verified by a whole bunch of ancient documents that record similar events. Likewise through archaeology many discoveries have been made that have backed up the biblical accounts (For example the Pool of Siloam from John 9 has been discovered fairly recently). There are also other documents that support the evidence that the biblical account is true. There are so many books on the subject! Do some research! If you're interested I did an essay on the accuracy of the gospel of Luke for school, I could send it to you if you comment below.
The bible is made from eye witness sources. In history, these sources are the most reliable (How can you get more reliable then people who have seen it?). Adding to that is the fact that many of these Christians were persecuted and killed for their faith. If they had simply lied about it all, why would they be willing to die for it? They also recorded things that would have been embarrassing for them (e.g. Peter's denial of Christ and the women being the first to find the tomb empty, because at that time the accounts given by women were considered far less reliable).
- Evidence within the bible itself
Another thing to consider is that the prophecies in the bible have all been fulfilled, except for those about the end times. Jesus fulfilled all the prophecies about him, even from hundreds of years before his birth. Many of these prophecies couldn't have been fulfilled on purpose if Jesus was just a man (Like where he was born, Herod killing the children, how he died and other things), and some of the key points are verified by other documents at the time.
- Evidence in our lives
Making our proofs out of what we see and feel is often unreliable and flawed - since we taint those things with our own perspectives, ideas, hopes and dreams. Nevertheless it is clear that the bible, and God, has had a massive impact on people throughout history. Christianity has been one of the biggest influences on the world we live in - yet if God doesn't exist it should simply be considered foolishness (e.g. people don't come back to life). Even though God has chosen the foolish things of the world to shame the wise (1 Corinthians 1:27), he has still had a massive impact on people and the world. If God doesn't exist then there is no reason that the bible should have been accepted at all.
The bible has changed peoples lives - talk to Christians around, you should be able to see this. God through Jesus offers complete forgiveness and he has transformed lives through his Holy Spirit.
With all this in mind...
If God is real, and if he is the God of the bible then how do we need to respond? We need to realise that we are sinful and have rebelled against him. That means we deserve his punishment eternally (hell). It is only from that position that we can realise that we need Jesus. We are utterly sinful, yet he was perfect. He (God) came into the world as a man, lived perfectly and then died in our place. On the cross he took the sin of all who put their faith in him - he took our sin and he took God's wrath for it so that we can be forgiven. That's the gospel! Jesus alone can deal with our sin and he calls us to give it up by repenting (turning away from sin and living for God) and by putting our faith in him - trusting that he has done it.
This brings it back to you. Do you accept this as truth? It is the truth, regardless of if you accept it.
- If you are a Christian then great! Are you telling people about Jesus and all he has done? Are you asking questions and seeking to grow and more more to know God and all he has done for you?
- If you're unsure about it all then keep reading! Keep asking questions, keep seeking answers and don't give up until you are completely satisfied!
- If you don't accept it, if you claim either that God doesn't exist or that he isn't the God of the bible, then don't be so proud and stubborn as to disregard this straight away. You could be wrong, so consider why you believe what you believe. What evidence do you have to offer for whatever faith you hold (whether that be the faith that 'science' is right, or faith in another 'god')? Keep asking questions, keep testing things and seeking the truth!
I hope that was helpful to read through and think about.