Disclaimer: while I strive for accuracy and completeness, the science in this post is a small snapshot of all the different ways we have of coming to the conclusions that currently stand as scientific knowledge. While it's useful to understand, it's by no means a substitute for real knowledge, and I encourage everyone to inform themselves on the processes involved.
This is something that comes up again and again, believers asking "what if evolution is not true?" when unsatisfied with any answer containing the word. There is a reason that evolution is an answer for many questions relating to humans, we are biological creatures and thus we are under the constraints that the evolutionary process has gone through. But to creationists, they can't grasp the concept. It stems from the fallacy that if evolution isn't real, that creationism is not only an alternative but the alternative. Evolution happened, there isn't any debate in the scientific community about this. There is debate about the mode it took, but that's another story. It's time to play the game, would the removal of evolution from theory make creationism any more plausible?
Absolute dating is normally done with one of many radioactive substances. The rationale is that certain substances are unstable and thus the nuclide decays. By knowing the decay rates and testing for those substances in the rock, the age can be determined with varying degrees of accuracy. The technique can be tested against artefacts of a known time to test it's accuracy, as well as being tested against relative dating where it should follow that rocks in a lower geological column show up as older using the test than rocks at the top. Likewise there are multiple radiometric dating tests, and dates can be cross-checked against each other.
From this the oldest substance found on earth was some zircon that dated to 4.404 billion years old (+/- 8MYA). We've found meteorites that date to around 4.57 billion years, which is being taken as the upper age for the solar system. So taking out evolution does not at all change the fact that the earth is old.
Next up is the fossil record. Certain species lived at certain times, and this can be found out by dating the rocks where fossils are found. While some fossils can be eroded and deposited in higher strata, it can't go the other way. Looking at the fossil record, life came to this earth sometime in the first billion years of it's existence, and it was in a simple form. Complex organisms didn't come about until around 550MYA, and this can be seen in the geological columns. In the series Life On Earth, Attenborough showed a geological shelf in Morocco where by going further back in time the fossil record and life forms became progressively simpler until one stage where no more fossils existed in the rocks. This does not assume evolution happened (though it's a damn fine explanation), it merely shows that life of certain types have existed at certain times.
Another geological phenomena is that in the same geological shelf, rocks from multiple environments are seen on top of the other. Why would an area go from a reef to a tropical forest, to a temperate lagoon all on the same time? The answer is the continents are moving. Each continent is sitting on a plate, and that plate moves along the mantle. For instance the plate that Australia is sitting on is moving north at the face rate of 10cm a year. Plates can collide, thus shooting up mountains as we can see in the Himalayas. So by looking at geological columns that have been exposed through various means, we can trace back through time that area's geological history. We can see that once Australia, Antarctica, South America and Africa where all connected and we can work out just when that was through movement rates. This provides a look back into the land's past hundreds of millions of years.
So by now it should be established that even IF evolution didn't happen, the earth is around 4.5 billion years old and life has been on earth for around 80% of that time in various forms. It does not look good for young earth creationism even without the theory that species over time gradually change through mutation and natural selection.
Great balls of fire
Next stop is astrophysics. Astronomers predict the age of the universe to be 13.7 billion years old. Now lets again remove any assumption of evolution from astrophysics (it takes away nothing for the record). The Sun is a big fusion machine, it converts hydrogen into helium in it's core. By working out the rate of which hydrogen is fused into helium, an age can be worked out. Using this technique, the age of the sun is ~4.57 billion years old, which is consistent with the age of meteorites found that would have formed during the birth of the solar system.
Proxima Centauri is the nearest observed star to the sun. To calculate how far it is away, it's a case of simple trigonometry. By taking the angle to the star at one point of the year, then taking another 6 months later when we are on the other side of the sun, we can make a simple triangle. And by knowing two angles and one side (the diameter of orbit), the distance can be calculated mathematically. And the star is 4.2 light years away. Likewise we can calculate it's age in the same way we can calculate the sun's. And it's 4.85 billion years old, older than anything in our solar system. The universe just keeps getting older. Using parallax to determine a star's distance works to around 3000 light years. But a relationship between luminosity, distance and star type can be established, we call this main sequencing. So by taking a star's brightness and it's type, it's distance away from earth can be determined.
The furthest observed galaxy is 13.2 billion light years away. That means we are seeing light from that galaxy that was emitted 13.2 billion years ago. For objects this far away red-shifting is used. As the universe is expanding, the distance light from distance galaxies has to travel further and thus the photon of light becomes more red the further it travels. The oldest star is known as HE 1523-0901 and it's estimated that it's around 13.2 billion years old. It's in our galaxy as well! A NASA probe was able to measure the background levels of radiation in the universe, and from there based on the assumption that the laws of physics are constant the age of the universe is calculated at 13.7 billion years. There are other methods in determining this age too, it's not only the cosmic background radiation. Of course every time we've put an age on the universe, it's been found to be older than we've anticipated. So 13.7 billion years could be still underestimating the universes' age.
The living planet
Final stop is at biology. Now scientists believe life on earth has been for about 3.5 billion years, and complex life for about 700 million years. This is based on the age of fossils. What we have is the emergence and decline of species, we have the progression of bodies from invertebrates to vertebrates, jawless to jawed fossils, the gradual emergence of amphibians, then reptiles, the rise and fall of the dinosaurs, and finally the rise of mammals and birds. None of that assumes evolution, though evolution explains it so nicely. Now let's look at a couple of instances of dating in nature.
The first is a technique called dendrochronology, or counting tree rings. During the year, each tree experiences growth faster in the summer than winter. It's a yearly cycle and it results in rings. So the age of a tree can be determined by the number of rings it has. Since each season isn't the same, a good growth season means a bigger ring than a poor growth season. By taking patterns of several years from one tree, the same pattern can be found in others. So the early rings for one tree could be the most recent rings for another. So a 500 year old tree that matches it's first 5 rings with the 5 oldest rings on another 500 year old tree would show that the oldest tree came about 995 years ago. This technique has been used to go back around 10,000 years.
The second is about patterns in common ancestry. When a child is born, the DNA of the child contains half its mother's DNA and half its fathers. Its children will have half of if its DNA. So through this, common ancestry can be worked out by looking for patterns that both people share. If we all were created 6,000 years ago and came from one pair, it should be reflected in our mtDNA (DNA from our mother's lineage). Instead we see the last common ancestor of all humanity as around 140,000 years ago, with the first migration of modern day humans out of Africa as around 55,000 years ago. Not to mention by using the same technique, we go back 6 million years to our last common ancestor with chimpanzees.
So even in natural markers we have an old earth. Losing evolution would certainly not validate young earth creationism. It's not an "either or" situation, and creationists would be best served doing research to explain all evidence rather than just taking pot-shots at evolution. It just shows their profound ignorance of science to think that a young earth view rests solely on whether speciation is a product of natural selection. The scientific method may only look at small snapshots one at a time, but a scientific theory has to be consistent with all knowledge across many disciplines. It would be best served if believers learnt this now and stopped putting a myth across as a tangible alternative. It's just embarrassing.