Some Christians, such as Seventh Day Adventists, claim that the universe is only 6,000 years old, with fossils of dinosaurs planted in the ground and the light from galaxies which are more distant than 6,000 light-years pre-positioned enroute.
On one hand they say the existence of God can be known from looking at the things of His creation, just as Paul asserts in Romans 1:20. And on the other hand, they say the world's true age was faked, possibly as a test to weed out the true believers who rely on faith in the sacred scriptures from those who will be tempted to follow the evil human doctrines of science. What they never do is put the two claims together and conclude that God is a fake.
A fake past joined seamlessly with a real present can never be falsified. The line could be set at last Thursday just as validly as at 4004 BC. With no way to tell, it's a waste of time to assert any date.
What is the motivation for holding to a six thousand year old universe? Because these Christians have taken an isolated passage from the Bible that says "a thousand years is as a day to the Lord" and they have constructed a narrative that depicts human history as a "week" of these super-long "days". If the Earth is 6,000 years old, hence six symbolic "days", then we're on the cusp of the seventh day Sabbath rest, which is the Millennium to be ushered in by the Messiah.
Unfortunately, they can no longer use Archbishop Ussher's date of 4,004 BCE for creation, because the year 1996 has come and gone with no messianic age in sight. Frank Klassen, in The Reese Chronological Bible, gives the date of creation at 3976, hence the Millennium will begin in 2024.