Like millions of baseball fans, Kolek saw how impressive Finnegan was in 2 1/3 innings of relief in Kansas City's 9-8 win over the A's in 12 innings.
"What he did was amazing," Kolek said. "For someone 21 years old, it's crazy."
Seeing a member of his Draft class make a postseason impact fuels Kolek's desire to reach the big leagues.
"Oh yeah, of course," the 6-foot-5, 260-pounder said.
Advancement, however, will come in time.
The Marlins aren't rushing a raw talent who has the makings to be a future ace. Kolek -- ranked second in the Marlins' system by MLB.com -- made nine appearances and eight starts for the Gulf Coast League Marlins; he was 0-3 with a 4.50 ERA. He threw 22 innings, struck out 18 and walked 13.
More than results, he is working on his overall game -- fielding his position and holding runners. In terms of his delivery, he creates a downward plane with his pitches, which will help him miss barrels of bats. The ease of his arm action, and power stuff are other reasons why the organization feels it has a future star.
Heading into 2015, a realistic starting part for the right-hander could be Class A Greensboro.
"I think he comes into Spring Training at least competing for a Greensboro job," said Marlins vice president of player development Marty Scott. "I can't see him any higher than that. If everything goes well, he could get an opportunity there."
Greensboro is the level just below Class A Jupiter of the Florida State League.
"It's something you really don't want to rush him on, and if he is ready, he will show it to us," Scott said. "If he needs more seasoning at extended spring [camp], that wouldn't be a setback to me."
Three months after being picked second overall, Kolek has shown flashes of why he is so touted. His physical presence and 95-plus-mph fastball are attention-grabbers. But he's also young. He turns 19 on Dec. 15. Adjusting to life in professional baseball is a big change from where he was raised about 90 minutes outside Houston.
"You're traveling a lot," Kolek said. "You've got to get used to the schedule, being here early and at the field until 4 o'clock. It's hot, and all that stuff. At the end of the day, it's all worth it."
Wednesday was another day that was all about business. Kolek was pitching two innings at noon, on a summer-hot day on a back field at the Mets' complex in Port St. Lucie, Fla. He struck out two and gave up one run in a game filled with mostly 17-19-year-olds.
On the Royals' playoff roster, meanwhile, Finnegan (17th overall pick) is already making a big league impact.
Kolek has known of Finnegan for a while. Although they never met, the Marlins' prospect had a commitment to TCU that he was prepared to honor if he hadn't signed with Miami.
A realistic arrival to the big leagues for Kolek is 2017, or after two more full Minor League seasons.
If that holds true, Kolek will be 21, or the same debut age as Finnegan.
For now, the right-hander is getting his first taste of what it takes to advance.
"I'm learning to just calm down," Kolek said. "Whenever I used to throw, I would just rear back and see how hard I could throw it. Now, things have changed a bit. Here, the hitters are smarter. It kind of just brings you down to earth, and makes you appreciate throwing the ball to where you want to throw it."