Trucks rolled down a ramp into the site with lumber and equipment, and about a dozen construction workers began cleaning the memorial area and installing protective wooden coverings over parts of the original foundation.
After six to eight weeks of preliminary work, concrete will be poured to create footings to support the "Reflecting Absence" design.
Gov. George Pataki last week called the event "a very important milestone," but no groundbreaking ceremony was planned for the next several weeks.
Officials said they wanted to meet a schedule to build the memorial by 2009.
Some Sept. 11 families that oppose the underground memorial design are trying to stop the work before it is set in concrete.
The Coalition of 9/11 Families last week filed a lawsuit charging that the memorial would damage the historic footprints. Preservation groups have made similar arguments in letters to rebuilding officials. A court hearing was scheduled Monday, and other family members planned a protest rally.
"There is always opportunity until concrete is poured," said Rosaleen Tallon, the sister of a firefighter killed in the 2001 terrorist attacks. Tallon began sleeping outside her brother Sean's firehouse across from the trade center site last week, and said Monday's construction work wouldn't stop her protest.
The "Reflecting Absence" design, by architect Michael Arad, was chosen two years ago out of more than 5,200 competition entries. It marks the fallen towers near their footprints with two stone reflecting pools at street level, surrounded by trees. The pools go 70 feet below ground, where visitors find surrounding each pool the names of the nearly 3,000 people killed in the 2001 attacks and the 1993 trade center bombing.
Families have said the memorial would dishonor the dead by placing their names below street level and might be difficult to evacuate quickly.
Stefan Pryor, president of the Lower Manhattan Development Corp., the agency in charge of Ground Zero rebuilding, said the design would "fulfill the highest standards of both safety and beauty." He said the agency would continue to hear family members' concerns.
A private foundation still has hundreds of millions of dollars to raise to build the memorial and a museum. A $490 million budget will be reevaluated by the project's contractor over the next few months.
The World Trade Center Memorial Foundation has raised more than $100 million of a $500 million goal; it still has not calculated the costs of operating the facility.
Foundation president Gretchen Dykstra said the beginning of construction should jump-start fundraising and quiet skeptics who thought no plans would be realized at the site.