A steel beam from the World Trade Center’s fallen South Tower was displayed Monday at a Long Island education center, where hundreds of families devastated by 9/11 tearfully flocked to the mobile memorial.

“We can’t forget,” said a weeping Rosemary Cain, the mother of slain Sept. 11 FDNY firefighter George Cain, to The Post.

Cain was brought to tears at the sight of the 21-foot-long, 16,000-pound steel beam, which a police pipe band somberly escorted as it was hauled to the Lieutenant Michael P. Murphy Navy SEAL Museum in Suffolk County on a special truck as part of a cross-country tour. 

Cain recalled how her 35-year-old son was a “happy bachelor” and avid skier who would have turned 60 next week, had it not been for the 2001 terror attack.

The Ladder 7 Bravest was killed by the collapsing skyscraper while evacuating the nearby Marriott Downtown hotel with members of his 29th Street firehouse.

“There are times when you do feel that people have forgotten and society has forgotten,” Cain said.

The beam was brought to the Sayville site for the day by the Tunnel To Towers organization and the museum.

The event was part of Tunnel To Towers’ “Steel Across America” tour, which is making 35 cross-country stops in the coming weeks.

The goal is to physically remind the nation of the sacrifices made by those such as George Cain on the upcoming 25th anniversary of the terror attack. 

“We’ll make sure people realize when they put their hand on that steel, that there was a tremendous sacrifice made that day,” said Tunnel to Towers’ founder Frank Siller, who lost his younger brother, FDNY member Stephen, in the South Tower.

“That’s what we want all over the United States.’’

Siller and the organization have spent the past quarter-century fundraising and supporting the military and first-responder community through philanthropic gestures such as paying mortgages for families of those lost in the line of duty.

The Murphy Museum was the third stop on the newly launched tour, following Ground Zero in Lower Manhattan and Fort Wadsworth on Staten Island.

Stephen Siller’s son, Stephen Jr., has already been overpowered by emotion from the initiative.

“You can feel the weight of that day when you see the steel beam,” said Stephen, who lost his father when he was just a 9-month-old infant and now works full time for Tunnel to Towers.

He said he was truly touched to see a nearly hourlong line snake around the museum grounds, filled with people waiting to pay their respects.

“We’re indebted to places like this,” Siller said of Long Island. 

“They really keep our foundation alive and going strong.”

September 11, 2001, especially hits home at the museum, according to executive director and former SEAL Chris Wylie.

He said an estimated 75% to 80% of weekly visitors – including children – have an unfortunate connection to the dark day.

The same is true for Medal of Honor recipient Murphy, who died wearing an FDNY patch on his uniform during the ill-fated “Operation Red Wings” of 2005, which the 2013 film “Lone Survivor” portrayed. 

The Patchogue-born lieutenant, nicknamed “The Protector” while a teen lifeguard at Lake Ronkonkoma, was given the Fire Department arm sleeve accessory by two friends from his high school job, Jimmy and Owen O’Callaghan, who later joined the FDNY.

“It was basically to remind them of why they were in Afghanistan,” said Murphy’s father, Dan, who added that many of his son’s warrior comrades also sported the patch.

“When Michael was killed, and they recovered Michael’s body, the SEALs cut the patch out of Michael’s uniform, had it cleaned with the blood and everything.”

Murphy, who was in the middle of Basic Underwater Demolition/SEAL training when 9/11 occurred, had his patch posthumously presented to the FDNY along with a SEAL Trident.

The 29-year-old deliberately exposed himself to Taliban fire to call in reinforcements to try saving his four-man team, of which only Marcus Luttrell survived. 

“He wore it on every mission,” Dan said of his son’s FDNY patch.

Dan visits Michael’s grave at Calverton National Cemetery twice a week to keep his boy abreast of what’s happening at the museum.

The beam will next travel to the 9/11 crash site of Flt. 93 in Shanksville, Pa., on Thursday to honor the brave passengers who stormed the cockpit and fought the Washington, DC-bound hijackers to the death.

“When thousands and thousands of people get to see [the beam], maybe that will spark some resurgence of patriotism and more respect for what happened that day,” Cain said.

“And make sure that doesn’t happen again.”