So, let's for a minute suppose there was an Omega point. How does this prove that a god exists?
This has already been discussed:
As Prof. Frank J. Tipler noted, "Any cosmology with unlimited progress will end in God." (See Anthony Liversidge, "Frank Tipler--physicist--Interview," Omni, Vol. 17, Issue 1 [October 1994], pp. 89 ff.) This means, e.g., that any form of immortality necessarily entails the existence of the capital-G God, in the sense of an omniscient, omnipotent and personal being with infinite computational resources. This is mathematically unavoidable, for the reason that any finite state will eventually undergo the Poincaré cycle per the Poincaré recurrence theorem. This is very easy to see by considering the simple example of two bits, which have only four possible states (i.e., 2^2): hence, once these four states have been exhausted, states will have to recur. What that means is that any finite state can only have a finite number of experiences (i.e., different states), because any finite state will eventually start to repeat.
Thus, immortality is logically inseparable from the existence of the capital-G God, since mathematically, immortality requires the existence of either an infinite computational state or a finite state which diverges to an infinite computational state (i.e., diverging to literal Godhead in all its fullness), thus allowing for states never repeating and hence an infinite number of experiences.
Furthermore, any universal Turing machine is equivalent to any other universal Turing machine, as any universal Turing machine can perfectly emulate any other Turing machine, and indeed, anything that can logically exist. Since one of the traditional quidditative definitions of God is having an infinite mind, then by definition God would be a universal Turing machine, and thus if a universal Turing machine existed, apodictically it would be God.
Regarding the equivalence of God and the Omega Point, Prof. Tipler has published on this equivalence in the following peer-reviewed academic journal, which is the world's leading journal on science and religion: Frank J. Tipler, "The Omega Point as Eschaton: Answers to Pannenberg's Questions for Scientists," Zygon: Journal of Religion & Science, Vol. 24, Issue 2 (June 1989), pp. 217-253; doi:10.1111/j.1467-9744.1989.tb01112.x; available on the Theophysics website.
The Omega Point is omniscient, having an infinite amount of information and knowing all that is logically possible to be known; it is omnipotent, having an infinite amount of energy and power; and it is omnipresent, consisting of all that exists. As well, as Stephen Hawking proved, the singularity is not in spacetime, but rather is the boundary of space and time (see S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time [London: Cambridge University Press, 1973], pp. 217-221).
The Schmidt b-boundary has been shown to yield a topology in which the cosmological singularity is not Hausdorff separated from the points in spacetime, meaning that it is not possible to put an open set of points between the cosmological singularity and *any* point in spacetime proper. That is, the cosmological singularity has infinite nearness to every point in spacetime.
So the Omega Point is transcendent to, yet immanent in, space and time.
Additionally, the cosmological singularity consists of a three-part structure: the final singularity (i.e., the Omega Point), the all-presents singularity (which exists at all times at the edge of the multiverse), and the initial singularity (i.e., the beginning of the Big Bang). These three distinct parts which perform different physical functions in bringing about and sustaining existence are actually one singularity which connects the entirety of the multiverse.
And given an infinite amount of computational resources, per the Bekenstein Bound, recreating the exact quantum state of our present universe is trivial, requiring at most a mere 10^123 bits (the number which Roger Penrose calculated), or at most a mere 2^10^123 bits for every different quantum configuration of the universe logically possible (i.e., the multiverse in its entirety up to this point in universal history). So the Omega Point will be able to resurrect us using merely an infinitesimally small amount of total computational resources: indeed, the multiversal resurrection will occur between 10^-10^10 and 10^-10^123 seconds before the Omega Point is reached, as the computational capacity of the universe at that stage will be great enough that doing so will require only a trivial amount of total computational resources.
So to recapitulate:
1.) The Omega Point (or, for that matter, the society near the Omega Point) can trivially perform the universal resurrection of the dead, upon which the people resurrected can live eternally in literal heaven, i.e., paradise.
2.) The Omega Point is omniscient.
3.) The Omega Point is omnipresent.
4.) The Omega Point is omnipotent.
5.) The cosmological singularity is a triune structure, of which the Omega Point is one component.
6.) The cosmological singularity is transcendent to, yet immanent in, space and time.
7.) The cosmological singularity is the only achieved (actually existing) infinity.
8.) The Omega Point creates the universe and all of existence.
Those are all the main physical properties that have been claimed for God in traditional Christian theology. There are many other congruities between the Omega Point cosmology and Christianity. Below are listed just some of them:
1.) We are gods: John 10:34 (Jesus is quoting Psalm 82:6).
2.) We are God and God is us: Matthew 25:31-46.
3.) We live inside of God: Acts 17:24-28.
4.) God is everything and inside of everything: Colossians 3:11; Jeremiah 23:24.
5.) We are members in the body of Christ: Romans 12:4,5; 1 Corinthians 6:15-19; 12:12-27; Ephesians 4:25.
6.) We are one in Christ: Galatians 3:28.
7.) God is all: Ephesians 1:23; 4:4-6.
8.) God is light: 1 John 1:5; John 8:12.
9.) We have existed before the foundation of the world: Matthew 25:34; Luke 1:70; 11:50; Ephesians 1:4; 2 Timothy 1:9; Isaiah 40:21.
10.) Jesus has existed before the foundation of the world: John 17:24; Revelation 13:8.
11.) The reality of multiple worlds: John 18:36; Hebrews 1:1,2; 11:3.
12.) God is the son of man: Matthew 8:20; 9:6; 10:23; 11:19; 12:18; 12:32; 12:40; 13:37; 13:41; 16:13; 16:27,28; 17:9; 17:12; 17:22; 18:11; 19:28; 20:18; 20:28; 24:27; 24:30; 24:37; 24:39; 24:44; 25:13; 25:31; 26:2; 26:24; 26:45; 26:64. (This is just listing how many times Jesus referred to himself as the Son of Man in the Gospel of Matthew, although he refers to himself as this throughout the Gospels. It was the favorite phrase that he used to refer to himself.)
How item Nos. 9 and 10 relate is that within Prof. Tipler's Omega Point Theory the universe is brought into being by the Omega Point, as the end-state of the universe causally brings about the beginning state, i.e., the Big Bang singularity (since in physics it's just as accurate to say that causation goes from future to past events: viz., the principle of least action; and unitarity). Another way of stating it is that in the Omega Point cosmology, the Omega Point is the fundamental existential and mathematical entity, from which all of reality derives. Indeed, within the Omega Point Theory, the Big Bang singularity and the Omega Point singularity are actually just different functions of the same singularity. Further, anything which at any time will exist will simply be a subset of what is rendered in the Omega Point.