Err... even if we could time travel, I don't think it would be such a wise thing to do... :/
Back on topic now...
Here's a simple (flawed?) logic test I think disproves the possibility of time travel: There is an infinite amount of time from now until... the end of time. That gives someone an infinite amount of time to not only work out how to time travel, but to also share their invention with the rest of the possible universe. However, seeing as our lives have not been bombarded with approximately billions upon billions (no more than 10^26) random time travelers, I'd argue that time travel is impossible.
Anyways... back to the subject of God... just because "pain" and "evil" exists, it doesn't deny the existence of (a) God. If anything, it only denies the existence of ONE kind of God: the "all loving" variety. Furthermore, "bad" and "evil" are merely relative terms we humans construct, and I'd imagine (a) God to be above aligning Him/Herself with our "primitive" human constructs.
Consider for example a world where EVERYONE has all the same things (same possessions, same qualities, same flaws, etc), except that one group of people own BMWs and another group doesn't. The ones who don't own BMWs would consider their lives to be the lesser-off of the lot... and worse, would probably use their lack of BMW ownership as proof that (a) God doesn't exist... because, like, if God DID exist, S/He wouldn't have allowed them to live without BMWs, right?
The fact that people die does not deny (nor prove, for that matter) that (a) God exists. Frankly it's no different than saying that because if, say, your pet died, it means that your own parents don't exist... because if your parents are supposed to be loving and caring, they are supposed to protect you always and never put you through any pain in life, and therefore wouldn't have ALLOWED your pets to die. Yes I realize how silly this sounds, but that's exactly the point I'm trying to get at; it's equally silly sounding to say "just because people are put through pain and misery, God must not exist".
There are plenty of ways (a) God could exist, despite the fact that logical discussion can explain away certain types of Gods. Look up "Deism", as well as the Aristotelian view of (a) god. Those two camps tend to use Logic to surmise the possibility of an existence of (a) God. Then there's also what Jakob Böhme thought of when he pondered what God was like.
Personally, I believe (a) God exists. I'd like to think it's "THE" God... but personally I think God is more than any one particular God. In fact, I feel as if ALL religions that discuss the idea of a "head" or "top tier" God/Creator are all basically worshiping the same God. The best way I can explain my belief in God is that God is the set--as in mathematical sets, used in set theory--that contains the union of the Universal set {U} and is complement {U'}, where this universe and everything else that "exists" within it is a subset of the Universal set, and everything that doesn't "exist" is a subset of U'.
And I don't think this concept of God that I described can be "disproven", as it's merely the way I observe the manner by which the universe as we know it "exists", HOW it "exists" and WHERE it "exists", as well as whether anyone can actually say {U'} (aka U-complement) DOESN'T exist. But then again, if anyone says U-complement DOESN'T exist, then they don't know what mathematical sets are and the rules governing them. ... Unless maybe there's something
*I* missed; to which, correct me if I'm wrong.
Ultimately though, depending on how you want to define it, there is no way to conclusively prove that (a) God exists or not. You can only try to postulate whether or not a
particular variety of (a) God exists and see if it can be logically proven, disproven, or left alone. But frankly, I'd say that this universe itself has made the decision for us concerning the existence of God: the universe is agnostic.