Kostin, 18, selected by St. Louis with the 31st pick, took his first step toward that goal during Blues development camp last week. Still not cleared for contact following shoulder surgery in mid-January, he was unable to take part in scrimmages but did display some of his high-end skills during on-ice drills.
"It was very difficult, but I've worked very hard to get back in shape," Kostin said of his recovery. "And I'm practicing, getting ready to play. I'm at 100 percent now, ready to play in the NHL."
Kostin signed a three-year entry-level contract with St. Louis on Wednesday.
The Blues traded back into the first round for the chance to draft Kostin, sending forward Ryan Reaves and a 2017 second-round pick (No. 51) to the Pittsburgh Penguins for the 31st pick and center Oskar Sundqvist.
Kostin took another step toward his goal of playing in the NHL on Tuesday, when he was one of 42 players with Dynamo Moscow to become a free agent after the Kontinental Hockey League ruled the team didn't follow its contract obligations. His agent said on Twitter that Kostin would sign his entry-level contract with the Blues "in the coming days."
Kostin impressed immediately at development camp with his work ethic and skill set, including a hard, accurate shot.
"He's a hard worker. He's a hockey kid, a rink rat," Blues director of amateur scouting Bill Armstrong said. "One of the things that we liked about him is that on ice he plays a North American-style game. He's a big body (6-foot-3, 197 pounds) that plays a heavy game, so we're really intrigued. Not only that, but you get a skill package.
"Obviously, he's got some adjustments to make: How hard they play every night, the consistency factor over here. He's still a ways away, especially with the injury setting him back a little bit. But as you can see here in camp, some of the stuff he can do, he's got some really good potential and projection."
There's a bit more projection needed with Kostin than other prospects. He played eight games in the KHL last season, in part because of the shoulder injury, which he sustained playing for Russia during a pretournament game ahead of the World Junior A Challenge in December.
Although Kostin was limited during development camp, he is expected to play for the Blues at the NHL Prospect Tournament in Traverse City, Michigan, in September.