There is an abundance of evidence against a recent creation. It first must be pointed that there is a young-earth-creationist hypothesis that can explain any evidence of great age: Philip Gosse's Omphalos hypothesis, that the Universe was created with the appearance of great age. However, most Creationists have not had much taste for that hypothesis, and we can set it aside.
The evidence is
- Radiometric dating. It goes as far back as the origin of the Solar System, about 4.5 billion years ago.
- Dendrochronology: tree-ring dating. By correlating the rings of different trees, it has been possible to go back 10,000 years.
- Continental-drift extrapolation. One can find present-day rates with quasar and satellite observations, and compare it to the rates for the last few million years with radiometric dating. One finds good agreement.
- Milankovitch astronomical cycles. These are climate changes forced by changes in incoming sunlight due to the Earth's spin precession and the planets' perturbing each others' orbits. They have been used to improve on radiometric dates; the beginning of the Miocene has been pinned down to 23.03 million years ago with them.
- Helioseismology. The Sun has quakes in it, sunquakes, that travel through its interior. As with the Earth, these can be used to infer the Sun's internal structure. With the help of stellar-evolution models, one can find out how much of the Sun's hydrogen has been fused into helium, and get its age from that. The result is close to what one finds from meteorites. (The age of the Sun and the relativistic corrections in the EOS | A&A)
- Distances to stars and galaxies. These can be found with a variety of methods, yielding a "distance ladder" from closer to farther objects. Most of our Galaxy is farther away than the Biblically-expected distance of 6000 - 7500 light-years, and not surprisingly, other galaxies are even farther way.