The Mayans thought the world was created in 3114 BC. Lots of other cultures had similar "young" dates for the creation of Earth.
If you add up the dates in the Bible working backwards from known events, the world is only about 6,000 years old.
Ussher calculated the year of creation at 4,004 BC. Many others come up with very similar dates.
The idea that the world looks old is based on presuppostions. For example, you may assume the Earth must be older than x years, because you assume some geologic feature took x years to form. Well, maybe God just made that geologic feature. It's like saying, "We know this beach is x years old, because these rocks erode at a rate of y per year...."
But you assume God cannot make a beach.
As AV1661VET pointed out, God can make whatever He wants. He is not limited by naturalistic processes. When God wants to make a beach, He makes a beach. He doesn't need to make the cliffs of Dover and then have to wait patiently for the cliffs to erode over millions of years. He can just make it.
Even creationists are guilty of these presuppositions. For example, saying there was no coal or oil before the great flood because all the coal and oil is assumed to have formed in the flood. But God can make coal and oil if He wants. What proof do you have that God did not make any coal or oil in the original creation? The only proof is "We know because coal and oil are formed by natural processes...."
But it's circular reasoning. It's like saying "We know because we know". No you don't know. You were not there when the world was created to see what God made.
Saying "God did it" isn't an excuse because we don't understand natural processes. Rather, we say "God did it" because we believe the "natural processes" are in fact under God's control, and He is above the laws of nature itself, being their Creator. He can do anything.
To be fair, Atheists believe in the "miracle" of abiogenesis. This was proven a myth by Louis Pasteur. Everyone, including Atheists, knows that abiogenesis is impossible. But their faith is strong enough for them to say with confidence, "Nature did it". And how does that compare when we say "God did it"?
If you assume God needed billions of years to create the world, then you are limiting God and contradicting the Bible, which clearly states that death is the result of sin. Theistic evolution puts death before sin, along with a whole bunch of other problems that cannot possibly align with the Bible.
In summary, we are free to choose what we believe is true, based on our own study, experiences, and rationale. And I choose to believe that God created the world about 6,000 years ago.