Yes, of course people usually trust the US government. We do so every time we get on a plane, keep money in USD, or run Windows, MacOS, etc.
That doesn't mean the US was flawless before Trump. It had its flaws, just like any other government. But generally, they were trusted in scenarios like above, but also, for example, by diplomats to at least try to keep their word even across administrations, or by travellers not to be asked for bribes at the border.
People have become rather cynical and won't believe me, but still it is worth mentioning: before Trump, politicians, including the presidents, almost never lied. On occasion, they would try but fail to make good on a promise. Or they would err, or go to great lengths to avoid answering a question.
But actual lying, as in saying something wrong and repeating it even after it was pointed out to be wrong? It barely ever happened.