Yes your logic is accurate. So, lets say that there is an equal chance that God existed at the beginning of "time" and that a big ball of dust existed at the beginning of time.
Now, having established that one is just as likely as the other... which of those two options is more likely to have created the entire universe? Therefore, simple math dictates that God is a much higher probability.
Actually, neither would be more likely. It's common knowledge that, any given atom, can form a bond with any other compatible atom, until stability is reached. It is not at all unreasonable, to assume that atoms rearranged themselves (it happens in front of your eyes all the time). Don't forget about gravity: gravity is that attraction, that all matter has. The matter basically goes into a snowball effect, which would form planets, stars, entire galaxies, etc.
Also, the universe is extremely old: most of us would not comprehend, just how much time matter had, to rearrange itself into what we see today (and of course, rearranging would mean forming chemical bonds, gravitational attractions, etc). It's roughly 13.75 billion years old. Just try to fathom how long that is: If an 80 year old man repeated his life cycle, throughout the lifespan of the universe, then he would have lived 171,875,000 times!
Right but lets say its "possible" for the atoms to rearrange themselves, maybe a 1% chance... if we're being generous. It is 100% possible that an all powerful God (assuming He exists) created the universe.
Therefore if the odds of there being a God or there being Mass at the beginning of time are equal, then God is more likely as being the source for the creation of the universe!