An interesting way of framing the question. You mentioned *natural occurences* - Then I must ask: When did the sea level rise? I have lived for 17 years in Hawaii.
A good question. Has it risen? Even if we know as a scientific fact that the ice sheets are retreating in Antarctica and Greenland, should it be rising?
One thing that I have learned from these scientific prognostications, whether they happen or not, is the fascinating fact that when you kids and your grandchildren and great-grandchildren grow up, if this trend continues, the complete melt down of Greenland ice, in itself, will cause the sea to rise seven metres.
This story is not unlike cigarette related cancer. Prove it, said the tobacco producers. Of course, everybody knows that the odds of lung cancer increase exponentially if you consume this poison. Nevertheless, for legalistic purposes, it must be proven without the shadow of a doubt.
So you need proof. I can appreciate that. And the proof is that ice, lots of it, has been melting; that droughts, unprecedented for the last fifty years, are re-occurring with alarming frequency; that violent and destructive storms have been increasing in frequency; that bushfires, such as in Australia, have expanded in number and in magnitude.
All of this might not be noticeable on your beach but it has been occurring globally. Or, perhaps, you need a ten-year perspective on what has been happening to your surroundings, which is not easy to observe because of how we rapidly normalize change.