There are somethings in the Dhamma that have to be taken on "faith".
The best way I've heard this was put like this:
So I have never been to Australia. But, lets say I meet someone who lives there. They tell me about Australia. They also tell me about there trip to Oregon. I have been to Oregon and know what its like, and there description matches mine. Therefore due to the fact that I can verify they know what they are talking about, along with there accent and seeming knowledge of Australia, its fair for me to believe they are from Australia.
In the same way I am not enlightened nor do I have knowledge of past lives. But, I can verify that the Buddha knew what he was talking about in terms of Dukkha, Annica, and Annata. I can also see the truth of the Four Noble Truths, and the Noble 8 Fold Path. The more I practice this path, the more obvious the truth of the Buddha becomes. Therefore, I have no problems believing what the Buddha has to say about Nibbana or rebirth.