The OP asks if a literal Genesis creation can hold up, and to address that question a bit more, here is some of the evidence (off the top of my head) for why the Earth and the Universe are FAR older than mankind.
The examples I'll take here is a generous estimate (as greentwiga talks about almost 100,000 years since the creation, in contrast with the 6,000-10,000 years most literalists believe the Earth to be). So here is evidence that the Earth and the Universe is a lot more than 100,000 years old. The Earth is estimated to about 4 billion years old, and the Universe to about 13.7 billion years old.
But every time I mention 100,000 years, it is no less true for 6,000 year-old-Earth ideas.
- The Universe is big. Any light source more than 100,000 light years away must have existed more than 100,000 years ago, because light travels at light speed and travels 1 light year in 1 year (hence the name - but it's important to rememeber that light-year is a measure of distance). Our very closest neighbour galaxy (excluding the Milky Way and its satellite galaxies) is the Andromeda Galaxy. It is about 2.5 million light years away, so if the Universe was less than 2.5 million years old, light from Andromeda would not have reached us yet. There are other galaxies that are several billions of light years away.
- The Universe contains a lot of stars. There is an estimated 100 billion galaxies in the observable Universe. Each with 10-1,000 billion stars. If all those stars (a very modest estimate is 100 billion x 10 billion = 1,000,000,000,000,000,000,000 stars) were to be within a sphere of 100,000 years radius from the Earth, it would not be enough room. The heat and light from all those stars would be overwhelming. So it is clear that a lot of the objects we see are more than 100,000 light years away, and therefore emitted their light more than 100,000 years ago
- The Moon and other atmosphere-less bodies in our solar system has lots and lots and lots
(and lots!) of ancient impact craters from the early Solar System when accretion of mass meant a lot more asteroids and objects in the solar system. These have taken billions of years to crash into bodies, building up these bodies and marking them with countless craters. The "seas" or "mares" on the Moon's surface are gigantic plains from when parts of the Moon was molten from its formation and large impacts. If all that happened in the last 100,000 years, parts of the lunar surface would still be molten.
- The Earth's core is liquid. Although this at first sight might seem to indicate a young Earth, the nuclear processes that cause this are well understood. But the liquid core causes plate tectonics. Large continental plates drift around - some places they crash and form mountains (it can actually be measured that some mountain ranges are gaining height, but so slowly that it must have taken millions of years to form them)
- Other places continents recede from each other and there are volcanos in the gaps between them. The continents can easily be seen to fit (anyone can see that the Atlantic ocean is roughly the same width in the east-west direction and that the continents on either side seem to fit together). The speed at which the continents move away from each other means that we can calculate or estimate how long ago they were joined, and the answer is at least millions of years (I don't have the numbers in my head but they are available by a google search)
- On each of the receding continents there are species that are genetically similar, and the fossil record on both continents show some of the same species, and if you place the continents together, the fossils lie in bands across both continents, a further indication that they were indeed once joined. The age of the fossils is in agreement with the estimated time when the continents must have been joined based on their speed (a few centimeters per year) and distance (thousands of kilometers) today.
- The fossil record shows that species have evolved ever so slowly over eons of time. The geological Earth layers they lie in, DNA analysis of current species, radiological dating and a lot of other dating techniques confirm their age. There have been life on Earth for billions of years, and it has slowly evolved and diversified.
- The fossil record shows a gradual evolution of apes into various hominids, most of which died out eons ago, but some remained and evolved further and further over millions of years to become modern humans. There is no "missing link" - and the process is well documented and understood.
- The Universe expands. The redshifting of light ("stretching" light to longer wavelengths due to the expansion of space itself) is observed and confirmed for a hundred years now. The farther away a galaxy is, the more redshifted its light is. This means that the Universe must have been much smaller in the past (billions of years ago). One can observe the Cosmic Microwave Bacground Radiation, which is extremely red-shifted (to a temperature of only 2 Kelvins). These photons were released once the Universe cooled enough to become transparent gas instead of opaque plasma. It is evidence of a Universe that was so small (and therefore so dense) in the past that its temperature was high enough that it contained only plasma. Plasma is matter where the nuclei of atoms cannot hold on to their electrons so the electrons flow freely around. Big Bang or not, this is evidence that the Universe was once much much smaller and denser and hotter, and that this must have happened several billions of years ago.
- There are "standard candles" - events of specific luminosities in the Universe. For example if a white dwarf orbits a big star and "steals" matter from it, at some point the dwarf's mass will be above the critical limit and it will go off as a type Ia supernova. All these stars are the same mass when they go, they have a specific signature as to the development of their brightness, and they are a good way of measuring cosmic distances, because if an object of a certain luminosity is twice as far away, its brightness will be 1/4. These supernovae also confirm the fact that the Universe is BIG and that these events must therefore have happened millions or billions of years ago.
- We know how stars form. The accretion of hydrogen (and a bit of helium) from the Big Bang under gravity makes the gas "lumpy" and those "lumps" then gather more mass until they are large and massive enough to ignite fusion and start shining. This takes millions of years. If the Sun was formed naturally only 100,000 years ago, it would not be very stable yet. Of course God could have created the Sun as it is as well as create the natural processes that would create stars but not use them for anything else than confuse us...
Maybe he created us all 10 minutes ago with all our memories and signs of the world being older than 10 minutes, but that's not very likely, is it?
If you're going to believe Genesis over all the scientifically confirmed material, you will have to believe:
- that God planted photons coming towards us from the Andromeda Galaxy and all other galaxies in the middle of deep space, to give the illusion of a large Universe. If the Andromeda Galaxy actually exists we do not know because the light from it would only reach us in over 2 million years. So God must have created fake images of galaxies and stars.
- that God even planted things like redshift into these false images to make them appear more realistic, and he also planted extra bursts of photons to simulate supernovae and gamma ray bursts, but all these are fake as the Universe is far too young for light from real such events to have reached us.
- that God created the continents more or less as they are today, but made them fit together and move slowly away, AND created current species with DNA similarities (to simulate that they are related) on both sides, AND created fake fossils from a time that has never been, to further simulate the fact that they were once joined
- that God has buried fake fossils in specific layers of earth and rock to give the illusion of geological periods on Earth, and that he's been very meticulous in his work to avoid any fossil from being in a wrong layer, as that could cause us to suspect something was wrong with our theories of an old Earth
- that God created lots and lots of fake impact craters on every solar system body that has a thin (or no) atmosphere, and that he created indications of big impact craters on Earth, and then simulated how millions or billions of years of weathering and geological processes would make them look today, and made them so to appear ancient when they aren't
- that God even took the time to simulate billions of years worth of solar system action just for the heck of it - for example Neptune's moon Triton which is in a retrograde orbit, has one of the roundest (least elliptic) orbits we know. This is of course consistent with theories of billions of years of tidal forces and gravitational effects that show that retrograde orbits will be extremely circular and will decay until the moon splashes into Neptune. So God created Triton's orbit this way to, again, simulate an ancient solar system, but it's all a divine hoax.
- that God created mountain ranges where they would naturally form over millions of years, and made them grow slowly due to these natural mechanisms, but the mountains themselves were created where they are by God and made to look like mountains would if they formed naturally
If you are ready to believe all those things (or simply just put your fingers in your ears and go "lalalalalala" to centuries' worth of scientific evidence), then welcome to the wonderful world of ignorance. If ignorance is bliss then good for you.
But you would still be factually completely wrong to assume an Earth that is only tens or hundreds of thousands of years old.