There are several different lines of evidence for dark matter as well as a few of its properties.
1. The velocity curves for stars in galaxies.
If we look at the matter that is visible in galaxies: stars, nebulae, etc, we can use the known laws of gravity to determine the velocities to be expected in the orbits of the stars. This is a very straight-forward calculation that can be done at the undergraduate level, but the results of those calculations do not match the actual observations of those stars. Furthermore, this is true for every galaxy we have done the calculations for, which is thousands of them.
Now, at this point there are two primary ways to proceed: either assume the 'known' laws of gravity are wrong, or that there is some extra mass out there that was missed when we accounted for the visible matter.
2. Dynamics of galactic clusters.
We detect quite of few galactic clusters that are gravitationally bound. But, if we do our calculations based on the known laws of gravity and the visible matter, those clusters should NOT be gravitationally bound: there would be too little mass to keep the clusters together given the velocities we observe in those galaxies.
Again, there are two main ways to proceed: either change the laws of gravity or postulate some unseen matter there that makes up the difference to make the clusters bound.
It should be noted that 1 and 2 operate on very different scales of distance. 1 deals with the stars inside of galaxies and 2 deals with galaxies inside clusters. Often, these clusters of galaxies have hundreds to thousands of individual galaxies in them.
it should be noted that the extra mass required to make 1 and 2 consistent with the known laws of gravity are also consistent with each other. In other words, the extra mass required is the same when systems are looked at in two very different scales and with very different internal dynamics.
3. Large scale gravitational lensing.
When light goes past a large enough mass, the direction of its travel is changed. Again, based on the known laws we can predict how much the line of travel will change based on the amount of mass present and its distribution.
We know of many systems where there is gravitational lensing happening. Once again, if we use the amount of visible matter to predict the amount of change in the direction of light, the calculated results are not consistent with observations. And, again, there are two ways to proceed: either change the laws of gravity or postulate extra mass that isn't visible. And, once again, the amount of mass required to make the lensing calculations work is consistent with the amount of extra mass required in velocity curves and in galactic dynamics.
Also, the test via lensing is very different than the tests based on dyanamics. So this is a very different sort of system that gives, again, the same results.
4. Tight constraints on the laws of gravity.
Given the multiple successes of the laws of gravity used in the calculations within the solar system, any changes to the gravitational laws must have *very* small effects within our galaxy. Remember that Newton's laws were used to predict the existence of Neptune from the motions of Uranus, which didn't agree with the calculations done with the known masses in our solar system. Einstein's extension was even more successful and to more decimal places than Newton's, with no known counterexamples in any observation.
5. Small scale gravitational lensing (microlensing).
Here, the comparison with 3 is similar to the comparison between 2 and 1. Instead of looking at the large scale deviations of light passing by very large galaxies, we look at much small deviations based on light going past portions of galaxies. This method can actually be used to map out *where* the missing matter is and its density distribution. Once again, it is *possible* that this could be explained by a modified theory of gravity or via some extra mass.
And, indeed, a modified theory of gravity was proposed: it was called MOND. By adjusting some parameters in this theory, it was possible to explain thee previous observations while still not destroying the successes with the solar system results. This was possible, in part, because the distribution of the extra dark matter required in the above situations parallels the distribution of visible matter. So it was possible to modify the explanation of the gravitational force to align with what was seen.
6. Evidence from colliding galactic clusters.
The Bullet cluster is the first example of this, but others have also been found. In this, the observed gravitational lensing does NOT parallel the distribution of visible matter. Instead, as the clusters collide, the ordinary matter is slowed down due to gas pressure. The observed lensing doesn't come from areas where there is visible matter. Once again, we can use the lensing to plot out *where* the extra mass is and the amounts needed.
So, by this, we have eliminated the possible modifications to the law of gravity to explain these observations.
7. CMBR
The Cosmic Microwave Background Radiation is one of the most important sources of information for precision cosmology. With it, we have been able to establish the overall age of the universe, its expansion rate, and a number of other parameters that were unknown when I was young.
It turns out that 'ordinary' matter, which consists of protons, neutrons, and electrons, leaves a very specific signature on this background radiation. Because of this, we can determine very precisely how much 'baryonic matter' there is in the universe. The amount is, by the way, consistent with the visible matter we can see.
It also turns out that the CMBR records, in a different way, the *total* amount of 'matter' (defined by the property that its pressure is inversely related to its volume, like a gas). And guess what? The total amount of matter does NOT agree with the amount of baryonic matter! The difference is again consistent with the amount of extra matter required for both dynamic and lensing observations.
So, yes, we see many phenomena that we can measure in detail, from velocity curves, to lensing, to the background radiation. These *all* point to extra matter that we do not see: it is 'invisible'.
But we can go further. What sort of properties would this 'dark matter' have? One of the early proposals was the dark matter could be made from massive neutrinos. This was attractive for a number of reasons: we know neutrinos exist, we know they are quite numerous, and even if they had very small mass individually, the numbers of them could easily be enough to supply the needed gravitational effect. It was even found that neutrinos do, in fact, have small masses. Unfortunately, their masses were too small and simulations with them don't give the type of gravitational dynamics (in particular galaxy formation) that is actually seen. Nonetheless, the fact that neutrinos interact so weakly with light shows that 'dark matter' can fit into the known properties of subatomic particles.
Now, there are many proposals as to what the subatomic composition of dark matter might be. But that is a separate question from the *existence* of that dark matter, which is very well supported by multiple lines of observation.
Now, since you want to make an analogy between dark matter and deities, what actual observations and what tests, alternative proposals, and data do you have for the existence of any deity?
