Randy Smith, the Padres director of player development, said Tate has played in games in extended Spring Training in Arizona every day for the past week.
"He's getting better," Smith said. "He's starting to swing the bat and get his timing down. He's making progress there. You can see all the tools and athleticism."
Tate's professional debut has been delayed for a myriad of medical maladies, including a sports hernia, a broken jaw in an ATV accident, a sprained shoulder and a concussion after he was hit by a pitch in extended Spring Training.
The Padres had originally thought Tate would start his career with Class A Fort Wayne, but the concussion set him back.
There will be a week off next month, when extended Spring Training ends before the start of a mini-camp, to get players ready for short-season Eugene. Eugene opens its season on June 18.
Tate agreed to a club-record $6.25 million signing bonus a year ago.