That's an excellent question.
Some evidence has been offered already specific to the flood including evidence specific to the fossil record, that the size of the boat was sufficient for the cargo, etc.
But there are other reasons for believing the scriptures are true. Two primary evidences of God's involvement are miracles which demonstrate God's power and prophesies which can be authenticated over time which demonstrate God's foreknowledge.
There are numerous prophecies that can be reliably dated and their fulfillment noted. Some of which are being fulfilled in our time.
The evidence for various miracles are the testamonies of people who saw them. And some records of miracles are in secular works, such as the darkness in the final hours of Jesus' death on the cross.
Many of the prophets referred back to the books of Moses treating them as authentic. Therefore if you can accept Jesus or any of the later prophets as being true prophets, you can effectively use their reference as an authentication stamp of prior works.
There is no fossil evidence for the Flood. At all. As for the Ark being of sufficient size, I ran the numbers on the beast a year or two ago on these threads and there isn't sufficient room for a tenth of the animals that would be required to have one or seven pair of each species (no one has yet defined a "kind" so we'll ignore it).
Also, at 135 meters long (450 feet) the Ark is too large to be structurally sound. No wooden ships ever exceeded 90 meters (300 feet) as wood cannot handle the stresses associated with being waterborne. The Scriptural Flood has all the earmarks of a localized event that has been exagerated through story-telling over many generations.