You are risking mixing up two different things into an impossible unity.
Yes, science is about testing, experimenting, challenging and if required falsifying previous beliefs.
With respect I suggest it is you that is mixing up two different things. Science does not rest on belief. That would be religion.
Of course it is possible that hypotheses are formed and various people may come to the conclusion that one or another hypothesis is more likely. But this does not negate the opportunity for falsification of the hypothesis.
I agree that there is very good evidence historically for very significant shifts in climate, both warming, and including as recently as the 17th century, cooling which have had impacts on a global scale. Like you I set out to understand the potential for mankind to have been influencing the various weather patterns around the globe that we describe as climate (of course there is not and has never been a "global climate") out of concern for my children's future, but the more I looked the more was the AGW hypothesis falsified on the evidence.
There is simply no evidence that any rises in average temperatures anywhere on the plant in the last 100 years is in any way exceptional.
There is simply no evidence that any rises in sea level in the last 100 years is exceptional.
There is simply no evidence that there has been anything remotely like a greater incidence of exceptional weather "events".
These are all assertions made in an attempt to "prove" that "global warming" is happening. The evidence contradicts all of them.
If there is nothing exceptional happening, a hypothesis that posits that mankind is causing something exceptional is very clearly falsified.