The Bible, which is God’s infallible word, clearly teaches young earth creationism in its history of the world. It lays out how the universe was created in the space of six days, including the creation of man (Adam) on the sixth day. It then lays out a genealogical record to the time of the earthly ministry of the Lord Jesus Christ, from which can be deduced the intervening time between the first Adam (the natural father of all mankind) and the second Adam (i.e., the Lord Jesus Christ, the spiritual father of all elect mankind), of approximately 4000 years. This divine historical record is why young earth creationism should be believed.
As explained in the article at http://www.puritans.net/yec/interventionism.htm , natural data does not disprove young earth creationism. While we can be thankful for the advocacy of young earth creationism by the advocates of so called “Flood Geology”, we must dissent from it as explained at http://www.puritans.net/yec/flood.htm . Natural data simply cannot be used to determine the age of the world. We must depend upon divinely inspired history to know the age of the world, even as we must depend upon divinely inspired history to know the gospel of the Lord Jesus Christ. While natural data can yield some information to mankind, some information is simply outside its purview.
A brief review of Philip Henry Gosse’s Omphalos is at http://www.puritans.net/yec/omphalos.htm . I believe Gosse provides a model closer to the likely true explanation of origins in the young earth creationist framework.