A spokeswoman for Brine, which has been selling lacrosse equipment since the 1920s, had no comment when asked about the opportunity to develop headgear under the new standard.

The marketplace could be highly lucrative, as there are nearly 300,000 female lacrosse players in the United States, and the number is expanding rapidly. The number of American high schools with girls’ lacrosse teams increased by more than 31 percent from 2009 to 2014, according to U.S. Lacrosse.

But meeting the ASTM standard will be challenging. While the approved headgear cannot have a hard outer shell or sharp protruding parts, it is required to absorb the impact of a ball traveling 60 m.p.h. or a stick swung at 45 m.p.h. The headgear, which must be flexible enough to pass what is called a deformation test, also has to be compatible with protective eyewear, one of the sport’s few required pieces of equipment.

Kevin Davis, chief executive of the Performance Sports Group, the holding company for Cascade, said his engineers were intrigued by an assignment that required a melding of the seemingly opposing dynamics of softness and hardness. The company has gone through multiple iterations of its headgear, especially after consulting with players.

Players who have not yet seen the new headgear are not sure how receptive they will be to it.

“I don’t think I will like it,” said Baylee Barker, a sophomore who plays for St. Stephen’s Episcopal School in Bradenton, Fla. “The headbands they’re making us wear in Florida now give me headaches. And on the package they come in, it’s literally in writing that they don’t prevent concussions.

“So I don’t see how they’re helping.”

Other schools have embraced headgear in some form and found a reduction in head injuries. After seven players on the girls’ lacrosse team at the Bullis School in Maryland sustained concussions in 2011, the team put every player in a rugby-style helmet that covered each player’s entire head. Five seasons later, the number of concussions — many of them caused by stick-to-head contact — has dropped dramatically.

“It’s had an impact and parents appreciate it,” the Bullis coach, Kathleen Lloyd, said of the headgear. “It might be more about raising awareness about contacting the head. There is a visual reminder.”