That's not required for the scientific method. The scientific method says put forth a theory, and see if predictions based on the theory are correct. It does not require absolute repeatability, it requires that predictions be correct. Repeatability in a lab is one way of doing that, but there are others. AGW theory passes that test with flying colors, because the predictions it makes have been correct. Your claim that something has to be repeatable in a lab to be science is nonsense.
Some things can't be repeated, generally due to scale. We can't affect the weather on the smaller scale, but that doesn't mean that meteorology isn't science. Or consider Astrophysics. It's impossible to do repeatable experiments in astrophysics. We can't adjust the properties of stars again and again and see what happens. However, no one would claim that astrophysics isn't science. Since your standard does say that, your standard is clearly not right.
Some specific null hypotheses are disproved in climate science. For example, a null hypothesis would be "CO2 doesn't affect climate". If that was the case, we would observe certain things. Since we don't observe those things, that particular null hypothesis is disproved.
You incorrectly state that "It's natural cycle!" is a null hypothesis. It's not. We know this because you can't even define what a "natural cycle" is, something that's necessary for a null hypothesis.
What's more, it's just assuming your conclusion. There's no reason to believe that's the default case.
If you want your alternate "it's a natural cycle" theory to be accepted, the burden of proof is on you. You need to make predictions based on it, and see those predictions come true. You can't simply declare that your quasi-religious belief is the default null hypothesis, because it isn't.
Please list for us the null hypothesis that stands in opposition your "It's a natural cycle!" alternate theory, and then tell us how you disprove that null hypothesis. After, of course, you specifically define what a "natural cycle" is, without using circular logic.