"It's kind of cool to see that," Cole said.
It's not only cool, but it provided a practical benefit. When Jordan was called up, Cole was named to take his place on the United States roster for Sunday's SiriusXM Futures All-Star Game at Citi Field.
"I feel like it's a great experience to be playing out here with basically the top players in the Minor Leagues, all up and down," Cole said. "You can learn a lot. You can watch people, talk to other people. Other people have great talents. Just watch and learn. That's the best way for me to learn -- is watching other people."
Cole has been a starter his whole life. He said he's only come out of the bullpen twice, both times before he turned pro. But in the top of the ninth, with one out and runners on first and second on Sunday, he was called upon to be the closer.
A called strikeout and a ground ball to second later, he walked off the mound with the save, as Team USA beat the World team, 4-2.
"It was kind of fun closing," Cole said with a smile. "But I'd still rather start."
The 21-year-old right-hander clearly has the arm. He has 99 strikeouts in 91 1/3 innings this season. He's currently ranked as the Nationals' No. 3 prospect by MLB.com. He was twice named the Carolina League's Pitcher of the Week in June, while going 4-1 with a 2.97 earned run average for the month. Overall, he's 5-3 with a 4.43 ERA.
"Basically, I feel like I've gotten to the point where my pitches are all there," Cole said. "Now, it's just basically consistency -- just making sure it's all one after another, not one day it's there and one day it's not. That's what I'm working on, right now."
The Nationals have stressed pitching in recent years. The top three in their rotation -- Jordan Zimmermann, Stephen Strasburg, Gio Gonzalez -- are as good as any team in baseball. The rapid rise of Taylor Jordan speaks to the depth in their system. All that, Cole says, works in his favor.
"It's exciting. The way I look at it, it makes me work harder," Cole said. "You've got great people coming up behind you, and you've got great people in front of you. So that makes me work harder. I want to see myself there. So I just keep working hard on the things I know I've got to do.
"I used to watch John Smoltz growing up. But now, it's more convenient to watch my own pitchers because the game's always on in the clubhouse -- so you end up watching them a lot more. And it's fun to watch."
Drafted in the fourth round by the Nationals in the 2010 First-Year Player Draft, Cole was traded to Oakland in the Gonzalez deal after the 2011 season. He was re-acquired for outfielder Mike Morse last January, and is hoping his next move will be up. He's seen how quickly it can happen.
Infielder Anthony Rendon played for Potomac in 2012, started this season at Harrisburg and made his Major League debut before the end of April.
"So it's exciting," Cole said. "He moved up to Double-A, and in a couple weeks he was in the big leagues. Everything's possible, so you just have to stick with it and keep working on the things you know you have to do."
Paul Hagen is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.