The universe appears "old", but it is still less than 10,000 years old

[Alex K]

Why I haz so much purrden of proof, while U can claim whatevers you want? Oh what the hellz, I'll write the leading arguments up shortly.

As far as creation cosmologies go, they by definition are worthless because God can predict everything and nothing.

So, the most important reasons why the scientific consensus says "there is a substance called Dark Matter", are:

• It explains rotation curves of galaxies nicely
  
• Together with vacuum energy, it produces a perfect match with the CMB power spectrum. No other known hypothesis does this.
  
• Fits to the first maximum of the CMB power spectrum and supernova data yield an excess in matter over the observed baryonic matter content of the universe
  
• We can observe the gravitational effects of dark matter via gravitational lensing, and observations like the Bullet cluster show that this cannot be taken care of by (only) modifying the laws of gravity
  
• Simulations of structure formation in the early universe using the dark matter hypothesis produce realistic late time structure
  

Note, the cold/warmish dark matter hypothesis explains all of these, and the second point should really count as a few dozen observations, since we are not only reproducing a number, but a highly nontrivial spectral curve. As a theoretical aside - dark matter is not a complicated or far out hypothesis at all. We already know three particle species which contribute to dark matter, and all one needs is one new type of particle not much unlike the ones we already know, with slightly higher mass (depending on how it's produced in the BB). It's really uncontroversial.