Gomez was joint top scorer in the Mexican league's Clausura championship this season, with 10 goals in 14 matches for Puebla, leading to his call-up to Bradley's preliminary World Cup squad.
"Hercules comes off the season very well," Bradley said at the squad's training camp at Princeton University. "Certainly we take notice of that and it's good to see how he'll fit in and play in this stretch."
The Los Angeles-born Gomez, who has played only twice for the national side, could feature in friendlies against Czech Republic on Tuesday and Turkey four days later.
Bradley needs to find a replacement for Davies, who was injured last October in a car accident that killed another passenger. He has resumed light training with his French club Sochaux but did not get medical clearance in time to make the squad.
The U.S. are drawn with England, Algeria and Slovenia in Group C at the finals starting on June 11.
Gomez's call-up to the 30-man provisional squad came after a decade-long journey through Major League Soccer (MLS) teams and lower-level U.S. clubs, before he hit the big time in Mexico, the country of his parents, where U.S. players are rare.
"It was a huge deal. I became only the second player in my club's history (to be top scorer)," said Gomez who, as befits his name, often strikes a strongman pose when he scores.
"They really took to me and treated me as one of their own. I was never treated like an outsider."
His Puebla team mates did, though, tease him. "I was always the 'soldier boy'," Gomez, 28, told Reuters. "They'd do the American soldier voice, or like in the movies, a robot, like (Arnold) Schwarzenegger."
Gomez, the oldest of five children born to Mexican immigrants, said he was realistic about his chances of making the cut when the squad is trimmed to 23 players.
"I definitely have 29 players in front of me," he said after a training session.
Gomez, who can score with his head and either foot, has attracted attention for his goal-scoring feats and said he had been getting offers from clubs.
"My agent handles those. I concentrate on the soccer and my only goal is this camp," he said.
Could he say where the offers were coming from? "Yes, but I'm only here to talk about U.S. soccer."
