When President Reagan first sent U.S. Marines into Beirut, their commander, Col. James Mead, told reporters that "I am not anticipating any need for us to use our weapons."

That was in August, 1982, when the Marines landed to form part of the international shield for the exit of the Palestine Liberation Organization.

Now, a little more than a year later, the Marines are in Lebanon on a second mission for Reagan that was supposed to be equally peaceful: providing a reassuring presence to the Lebanese army as it combats anti-government forces.

But the Marines have raised their firepower from M16 rifles to machine guns, to mortars, to 155-mm artillery shells, to the shells from the 5-inch gun fired yesterday from the Navy frigate USS Bowen on the waters off Beirut.

This steady escalation of firepower--which has occurred under the basic rule of engagement that the Marines can fire in self-defense--is expected to heighten the concern of those who have said the Marines were being ordered into a quagmire.

But Reagan administration officials stress that they must at least show, and sometimes use, impressive firepower to protect the Marines encamped near the Beirut airport and to deter Syria and its surrogates from stepping up their anti-government actions in Lebanon.

If shelling of the Marines continues, more counterfire is available, including that from the A6 light bombers aboard the nearby aircraft carrier Eisenhower.

Two F14 fighters from the Eisenhower flew reconnaissance missions over Beirut on Wednesday, apparently to help determine where the fire against the Marines was coming from.

Defense Department officials said there also has been discussion, but no decision, of sending the World War II battleship New Jersey from Central America to the Middle East so that its 16-inch guns could be brought into play in Lebanon if necessary.

Administration officials said yesterday that they hope they do not have to escalate the firepower further.

The decisions on how much firepower is enough to protect the Marines are made on a day-to-day basis, according to Pentagon officials.

They said yesterday's decision to fire the 5-inch gun on the Bowen, a 4,200-ton frigate of the Knox class commissioned in 1971, was made in response to a request for such support from the Marine commander in Beirut, Col. Timothy J. Geraghty.

Rear Adm. Jerry O. Tuttle, commander of Task Force 60, the ships off Beirut, had the authority to act on Geraghty's request without going up the chain of command, according to the Pentagon.

A Navy spokesman said that yesterday's shelling by the Bowen marked the first time since World War II that a U.S. Navy ship has engaged in shore bombardment from the Mediterranean, adding another twist to a highly unusual U.S. military deployment.

Unlike during the Vietnam war, the "gradual escalation" of firepower in Lebanon has not been triggered by the desire to kill enemy troops or support friendly ones on offensive operations.

Instead, the firepower has been defensive, in the sense that it is designed to protect Marines in virtually static positions on the ground in Beirut.

This "defensiveness" is further dramatized by the fact that the Pentagon recently sent a special unit, the Field Artillery School Target Acquisition Battery, to Beirut to track incoming mortars by radar to pinpoint their source.

The Marines then can fire warning illumination rounds against the positions before trying to destroy them with shells, mortars or naval gunfire.

One Marine general, who anguished when the Israeli troops in Lebanon harassed the Marines and who now is tormented by the pounding Marines are taking from the warring factions in Lebanon, called it a "cruel dilemma."

The Marines cannot leave without it being interpreted as "showing the white feather," he said, and yet they cannot go to the aid of the beleaguered Lebanese army without turning their mission into combat rather than "the presence" the president asked them to provide.

And sitting in bunkers and taking casualties is not what anybody had in mind on Sept. 29, 1982, when the Marines began their second Lebanese deployment under Reagan.

"This force is going in again," Defense Secretary Caspar W. Weinberger said at the time, "by the president's specific direction, not on a combat mission, but to help the new Lebanese government that has just taken office. They will go in to help them reassert their sovereignty."

After the Senate Foreign Relations Committee was briefed on that second mission, Sen. Paul E. Tsongas (D-Mass.) said something that is now bothering others, both in and out of government, as the Marines' position becomes increasingly dangerous.

"There's a sense that we're getting into a quagmire," Tsongas said a year ago. "We don't have a choice, but how are we going to get these troops out again once they go in?"