Olson, a left-hander who flew to Bradenton on Saturday and threw a side session in front of the club on Sunday, retired all three hitters he faced in the eighth on Monday.
"You only get one chance to make a first impression," manager Clint Hurdle said. "Low strikes, a few changeups, good downhill plane. We'll get him back out there as quick as we can."
The outing was an encouraging one for Olson, who hadn't been at his sharpest in his spring appearances with the Mariners. With Seattle, Olson had given up seven hits, three earned runs and four walks in five innings. The subpar results led the Mariners to place Olson on waivers last week.
"I just felt kind of slow starting out," Olson said. "The more innings that I get, the better comfort I'll get out on the field and the more I can get into a groove. I'm definitely looking forward to getting some more innings this week. I'd say that early on, I've definitely not pitched up to my abilities."
With the Pirates' dwindling left-handed options, Olson would seem to have a good chance at joining the club in Chicago on Opening Day. Joe Beimel and Brian Burres are the only lefties remaining in camp who are competing for bullpen spots.
Olson could be helped, too, by the fact that he is out of options. This means that the Pirates would risk losing Olson if the team does not put him on its 25-man roster.
"I think they brought me here for a reason," Olson said. "I'm going to come in here and continue to do what I can do, which is work hard. I'm going to try and capitalize on the opportunity. When I found out I was coming here, I was actually pretty excited."