Washington — Now that the shooting has started, it becomes harder for the United States -- or anyone else -- to settle the Falklands crisis by diplomacy instead of war, US experts agree.
Nonetheless, Britain and Argentina apparently still look toward US Secretary of State Alexander M. Haig Jr. to come up with fresh ideas that might allow both countries to compromise with some grace.
To that end, a strategy is beginning to develop here against the background of what State Department experts regard as two unfortunate but unavoidable facts:
First, the US regrets that the Organization of American States (OAS), at Argentine urging, is holding a special foreign ministers' meeting to consider the Falklands problem.
The obvious aim of Argentina is to muster Western Hemisphere support against Britain.
Second, US officials believe that neither leader -- Prime Minister Margaret Thatcher or Argentine President Leopoldo Fortunato Galtieri -- has much room for maneuver in the face of inflamed domestic opinion.
Argentine Foreign Minister Nicanor Costa Mendez is given high marks for intelligence and good sense by US officials who have worked with him. But he cannot exceed the writ handed to him by the Argentine military junta.
Some military action was held to be almost inevitable when the British fleet climaxed its 8,000-mile journey down across the Atlantic to the stormy waters off the base of South America.
''That fleet could not have sailed home without firing a shot,'' said an US expert, ''so long as Argentina continued to hold the islands.''
First priority, from the US point of view, is to confine military action to South Georgia island, insulating the Falklands themselves -- 800 miles southwest of Georgia -- from warfare.
Some sources say a successful assault on South Georgia might sufficiently assuage British pride enough to allow negotiations to bear fruit.
At the same time, US officials will strive within the OAS to convince Latin American nations, including Argentina, if possible, that invocation of the 1947 Rio treaty would not be in their best interests.
All signatories of the Rio pact are obliged under the treaty to go to the assistance of any member attacked by a power from outside the hemisphere.
This is the case that Buenos Aires no doubt hopes to make against the British. US experts indicate that the Reagan administration will take a different line within the OAS:
* Argentina, it may be stressed, was not attacked, but became the aggressor when it occupied the Falklands April 2 and South Georiga island the following day.
* The Rio treaty itself, in its first six articles, condemns war and the ''threat or use of force in any manner inconsistent with'' the charter of the United Nations.
* Self-determination of peoples is a UN principle to which OAS members subscribe. Invasion of the Falklands by Argentina deprived the 1,800 inhabitants of the islands, mostly British in origin, of this right.
Privately, a number of Latin American governments display acute discomfort over the Argentine tactic of forcing an open vote within the OAS. These governments dislike Argentina's record on human rights in general and specifically deplore what they regard as a denial of the Falkland islanders' rights to decide their own future.
The United States, in any case, will oppose invocation of the Rio treaty, sources say, although this would seem to cast the Reagan administration definitely on Britain's side.
Pro-Brisith sentiment is emerging in Congress, but the extent of possible US support for Britain has not been tested in debate.
''If the United States remained completely on the sidelines,'' said British Ambassador to Washington Sir Nicholas Henderson on the ABC television program ''This Week with David Brinkley'' Sunday, ''it would produce bitterness (in Britain).''
Mr. Costa Mendez, also speaking Sunday, said ''The United States has to (show) clearly that the United States also has an interest in Latin America.''
Sen. John Tower (R) of Texas, chairman of the Senate Armed Sevices Committee, said the US has ''no moral or practical obligation'' other than to support the British. ''Generally speaking,'' said Senator Tower on the Brinkley program, ''American public opinion is substantially pro-British.''