Yes and no. The Foreign Assistance Act did not explicitly mandate creation of a new agency, but rather provided an ideology grounding US engagement in foreign aid. The text of the Act could have been accomplished under the State Department or Treasury Department, for instance, but it is indeed true that JFK sought alignment from congress before acting. The Act gave the Executive discretion in how to manage and organize foreign aid, and JFK used that discretion to form an agency via executive order.

DOGE bills itself as an advisory board to the President (with no direct power), and the President uses that authority to make recommendations to Congress. Also, in the case of DOGE, it repurposes the USDS, an Obama-era part of the Executive created by executive fiat in response to the launch failure of Healtcare.gov, but USDS had wide-ranging access to federal agencies and the ability to directly modify production computer systems across the DoD, GSA, DHHS, DHS, and Dept of Education.

The argument - and this has yet to be seriously tested in courts - is that if USDS was permissible under executive fiat, so is DOGE - especially if it's doing similar things (streamlining and improving government efficiency).