Kennedy's Executive Order 10973 named the USAID. But read the first line carefully.

By virtue of the authority vested in me by the Foreign Assistance Act of 1961 (75 Stat. 424) and section 301 of title 3 of the United States Code, and as President of the United States, it is hereby ordered as follows:

This corresponds to a Congressional directive, the Foreign Assistance Act of 1961. That law required Kennedy to create a foreign aid organization to replace the hodgepodge then in existence. The law lists a wide range of international aid activities required by Congress and directs the president to put those functions under a single person.

The President may exercise any functions conferred upon him by this Act through such agency or officer of the United States Government as he shall direct. Tne head of any such agency or such officer may from time to time promulgate such rules and regulations as may be necessary to carry out such functions, and may delegate authority to perform any such functions, including, if he shall so specify, the authority successively to redelegate any of such functions to any of his subordinates. //

Such designation and authorization shall be in writing, shall be published in the Federal Register, shall be subject to such terms, conditions, and limitations as the President may deem advisable, and shall be revocable at any time by the President in whole or in part. //

From the beginning, the USAID administrator has required Senate approval and has had a budget.

Because Congress created the agency, President Trump will either gut it and leave the remnant alive or set off a direct conflict with Congress, which he may or may not want.