The first thing I'd do is commend you for your honest desire to know the truth about God. Down inside, you sense there must be more to life than you know right now, and you aren't content to ignore it. Perhaps Jesus had people like you in mind when He said, "Ask and it will be given to you; seek and you will find; knock and the door will be opened to you" (Matthew 7:7).
No, you can't put God in a test tube and "prove" He exists the same way you can prove a chemical exists (although nature's laws bear witness to His wisdom and power). But that doesn't mean faith is an illogical leap in the dark (as some have suggested). The reason is because God wants us to know Him and He has made this possible by revealing Himself to us.
How did He do this? He did it in a way that staggers my imagination: He became a man! Do you want to know what God is like? Look at Jesus Christ, because He was God in human flesh. If you have never done so, read carefully through one of the Gospels (such as John). As you do, ask God to show Himself to you as you discover Jesus for yourself.
Then don't be afraid to commit yourself to Him. Over the years I have met many outstanding scientists who were also strong believers in Christ. My prayer is that you will.