They don't. Only conspriracy nutcases tend to think so.
Israel is a very small country, small population and small economy. Just do the math.
.
That's really outrageous to say no matter who you are or where you are on the political spectrum. Although it depends on what exactly you mean by this. "Israel," and who can or will try to argue this, has an outsized influence on US and World politics. "The Israel Lobby." You want to talk about the Deep State, this is it. Who can argue that Jewish money largely funds both parties? Look at Trump sucking up to the Adelson widow now, he NEEDS the money. And since she, and they, are basically a 'one issue' people, the issue is of course Israel, they will want something for their money. - look at how Trump is talking about Israel now and in the past. People argue whether "Israel" controls the US... I say there's practically no difference between the two. Look at Netanyahu's orders for the US wrt the Gaza situation. Bibi says how it's going to go, Biden says ok. He talks about "red lines" but in practise it doesn't affect policy. The mild criticism is just for PR purposes.
On one hand they are extremely proud about their influence, but when it's pointed out it's a "conspiracy theory."
Israel is a small country but if you count the US as part of it things change.