USAID was created by an executive order, but then established by Congress in the Foreign Affairs Reform and Restructuring Act of 1998. Simple impoundment of funds violates the Impoundment Control Act of 1974. So Trump does not have the authority to just shut down USAID.

But here's the thing. He doesn't care. He has complete immunity for it. He isn't running for re-election. He believes that it is a political advantage for his legacy. He is effectively immune from impeachment until the midterm elections. If the court orders it re-funded, he re-hydrates it under his control, and is still politically ahead. And this informs most of his executive actions.