Paradox or not, as alpha is omnificent, it can create anything with no limits. Speaking of no limits, omega is an infinite force of destruction. Infinite meaning no limits. And since once omega gets loose it'll destroy everything, based on the fact both alpha and omega are omnipotent in regards to their respective concepts, assuming it'll destroy everything, including nonexistance and itself, isn't too much of a stretch. I say this because well, consider the following.
In order to be destroyed, something has to exist. Conversely, this mean it has to have been created in some way in order to exist.
Try as you might, you cannot deny the fact that nonexistance does technically exist. It's true.
In regards to the outcome thing, sure, I could believe that the alpha can't alter the free will of a living being. But what about altering the surroundings of said living beings?
Anything that contradicts itself isn't allowed. By anyone. If any action you're attempting contradicts itself through it's very existence - or lack thereof - then it doesn't make any sense, and is to be discarded.
Nonexistence does not exist. That's the definition of nonexistence. If it exists, then the term nonexistence doesn't apply anymore, because it exists. You stating that nonexistence exists made my head hurt >.<
And yes, if Alpha wanted Genocide dead, he could pop in and drop the Universal equivalent of a tactical nuke.
Alright you do make some good points, if you don't include the nonexistance thing, because if nonexistance didn't truly exist, would anything really NOT exist? Just a little food for thought.
Sadly, this isn't really going too far. So I'll change my strategy.
You yourself said that alpha can create universes in which a certain outcome is achieved. Such as genocide failing to destroy the multiverse. However, as alpha has no free will, it also creates universes in which the opposite outcome is achieved. Such as genocide succeeding. By this logic, the disadvantage every threat to the multiverse has, the multiverse's progressively infinite size, actually gives him an advantage. Genocide's goal is to destroy the multiverse by destroying balance and freeing omega who, once free, will destroy the entire multiverse. That's probably the same goal an infinite number of other genocides share. In other words, even if this genocide fails, another genocide will succeed. Essentially, the whole genocide thing is a one-sided struggle where the baddies win even when they lose.