There is one concept of forever however, that bothers me.
That is why Dr. Hawking himself said in an interview that:
"[T]o say 'I don’t know that God exists, therefore He doesn’t,' and to say 'In the face of my limited science, I declare that there is no afterlife,' in the face of the limited knowledge we have (brilliant as we can be), is actually a faith statement as 'ignorant' as some scientists accuse others of being."
I agree with Dr. Hawking in a way that it's needless defend or argue against religion / science as they both take equal amount of faith. An implication of the famous Godel's incompleteness theorem in math is that there's no true axiom in any science, math or model, because a statement cannot prove it's own validity. However, based on a set of presumed "axioms" science is wonderful and is for the betterment of our lives, but as much science as we have today, we just barely scratched surface of what's out there (or maybe not even close). Believing that something has always existed, something could come out of nothing, with no scientific proof is just another form of faith. Some people still believe that we, human beings naturally evolved from apes. To those, you need a biology lesson. The short answer is "we have no idea". People put words in Darwin's mouth, which is truly unfortunate. The correct statement is that we, humans, shared a common ancestor with apes, but as to how the evolution happened, science has only theories that are vastly unproven. Darwin died in 1882, and DNA wasn't ultimately discovered until Watson and Crick in 1950. Without the understanding of DNA, Darwin only theorized as much as he could.
This again, goes back to my issue that if something come out of nothing, we can potentially solve this problem of genes "popping into existence". Scientists' biggest puzzle is how can a gene that previously didn't exist suddenly "pop into existence"? It's like you are saying a machine writing it's own code, evolving from a windows 98 system into Windows 10 -- that's absurd. However, if you put infinity into the equation, then we may have a solution. It's not that things will forever repeat, but like you said, anything that can happen, will happen. I'd say you can think of the infinite universe, or "existence" as a Turing machine that runs permutations on an infinite set of variables. Although Windows 98 will not evolve into Windows 10 in finite time, but if you think of Windows 98's code as a problem, and the Turing machine's job is to figure out a solution and make it into Windows 10, then, given an infinite amount of time, the machine will find a solution and "evolve" it into Windows 10 - it will just take a gazillion years. Same thing with our DNA, if you believe that permutation of our genetic code is all it is, that the "universal logic" could potentially result in "humans" purely by chance.