There is no proof for God, in the sense that would compel all rational thinkers to agree that God exists, but there is at least some evidence, the robustness of which is up for debate. For example, there are the arguments from natural theology like the cosmological and design arguments. There is the historical case from sacred texts, such as the claims made about the life of Jesus in the Gospels. There is also a case to be made from personal experiences of miracles and divine contact. (I would go into a lot more depth here about the strengths and limitations of these cases, being fair in presenting the case of each side. How I approach this depends heavily on the question and on the syllabus.)
In conclusion, there is no way to prove God exists, but there is enough evidence that not all belief in God is irrational.