I haven't read anything that says opposition to AMGOT was the literal first act of the Provisional Government, but that doesn't mean it isn't true. The Comité français de Libération nationale (CFLN) in Algiers absolutely opposed the establishment of an Allied military government, and rejected the concept as soon as it was broached in discussion in 1943. Trading a German occupation for an Anglo-Saxon one was obviously not in De Gaulle's interest of restoring France into a strong, independent member of Allied Powers. It was also obviously not in De Gaulle's personal interest - both Churchill and Roosevelt questioned his popularity among the French population, and wanted an Allied interim government until a legitimate French leader could be found.

The Allies did not inform De Gaulle about D-Day and issued their own currency for soldiers landing in Normandy. They did not even recognize De Gaulle's provisional government until October 1944. Luckily for De Gaulle, among the Anglo-Saxon leaders only Roosevelt maintained his strong support for the AMGOT (Allied Military Government for Occupied Territories) plan, with Eisenhower in particular not keen to have the administration of France tacked on to his Overlord responsibilities. So the Provisional Government never had to fight particularly hard against the plan for an Allied military government, which was pretty much dead in the water the second De Gaulle landed and started imposing his own authority.

As to sources that would help you find more specific debates inside the provisional French government, you should see the Fuller book mentioned below, as well as Julian Hurstfield's America and the French Nation, 1939-1945, which I unfortunately do not have with me at the moment. If you can get a hold of it, Andrew A. Thomson's PhD thesis "Over There' 1944/45, Americans in the Liberation of France: Their Perceptions of, and Relations with France and the French" argues that the AMGOT idea actually did not die out in 1944. And if you read French, another useful book might be Régine Torrents's La France américaine: controverses de la Libération.

Sources:

Mary Louise Roberts, What Soldiers Do: Sex and the American GI In World War II France, 2013.

Robert Lynn Fuller, The Struggle for Cooperation: Liberated France and the American Military, 1944-1946, 2019.