And that mindset didn't come from a lack of ambition or imagination as much as an honest appraisal of the facts. Jankowski wasn't highly recruited as a high school senior, and he wound up choosing a school that has only had one player in its history make it to the Major Leagues.
Now, three years later, the fleet-footed outfielder has played himself into position to be the highest-drafted player in Stony Brook history, a possibility he still finds at least a little perplexing.
"Honestly, if someone asked me three years ago if I'd be projected this high, I would've said, 'No, not a chance.' It's always been my dream since I was little to play professional baseball, so it's really exciting," he said. "I'm trying to just finish out college first, and then after the season, I can enjoy it a little more. But as for now, you just kind of put it in the back of your mind and go out and play."
Jankowski, ranked No. 33 on MLB.com's Draft list, didn't have the high-school dilemma that many prospects experience. He went undrafted and unrecruited while at Lancaster Catholic in Pennsylvania -- perhaps because of his ability on the football field -- but decided that he wanted to play baseball in college.
The problem, he said, was that there wasn't a lot of interest. Stony Brook was the only Division I baseball program to offer him a scholarship, and only one other school -- a junior college in Florida -- presented a compelling alternative. For Jankowski, Stony Brook, located on Long Island, was the only choice.
"I had a couple offers from Division I colleges to play football," he said, "But my high school baseball coach told me, 'If you want to have a professional career, you've got a better shot in baseball than football.' He said, 'If you're going to go over the middle against a 250-pound linebacker, you're not going to last.' I took those words, and it's played out well. I think I made the right decision."
Did he ever. Jankowski is batting .350 for his college career and .393 through the first 50 games of his junior season, and he's stolen bases at an 87-percent clip (75-for-86). Stony Brook's center fielder considers himself a natural basestealer, but he's also learned to read the scouting reports.
And though he may have been a late bloomer, Jankowski set the stage for his success early. He can still remember tagging along for what he termed "two-a-days," which involved him practicing with his older brother's team before taking the field with kids his own age. Jankowski even had a tarp in his basement, and his father, Paul, would feed him soft toss every night to work on his swing.
Still, when Stony Brook came calling, Jankowski was a long way from a finished product. Coach Matt Senk, working through his 22nd season at the school, can remember the prospect fondly.
"We recruited what we knew was a great athlete, and the tool that jumped out most was his speed," he said. "Once he got here, he worked very diligently at his game, and our coaching staff did a tremendous job with him. We kind of saw him as our starting center fielder, but he struggled at the plate as a freshman. He kept working at it, had a great summer and has continually gotten better."
Jankowski has grown two inches and gained 20 pounds since enrolling at Stony Brook, and he credits the team's staff and strength coach for helping round out his game. That's a feather in the cap for a school that has only had one big leaguer -- Rangers closer Joe Nathan -- and 14 players selected in the Draft.
Stony Brook didn't make the leap to Division I until 2000, and it's had 10 players drafted since that development. Nathan recently donated $500,000 to the school for a new field that now bears his name, and Stony Brook feels like it's finally has the facilities to support a top-flight program.
"I'm just proud of the way the program continues to progress," said Nathan, who is now closing for the Rangers. "Each year, it gets better. As time goes on, they just keep making the right moves and put the right foot forward to make the program better. It shows with guys like [Travis] that the program is getting more exposure."
"It's tremendously gratifying," added Senk. "We were Division III when I first got here. We got better in those years, and in our last year, we made our first regional. We were ranked as high as eighth in the country, and then the decision was made to go to Division I. We had tremendous players and did a lot of winning through the transition years, and we've hit the floor running in Division I. It truly comes down to your players, and I'm so lucky to have had them and some great assistant coaches here."
Still, despite that improving pedigree, Stony Brook has never had a player drafted higher than the third round. The SeaWolves did have two players drafted last year -- Nick Tropeano and Patrick Cantwell -- and appear to have several players who could garner pro consideration in June.
Jankowski, who lists Ken Griffey Jr. and Josh Hamilton among his favorite players, knows that he has to get better to thrive in the pros. He's only hit five home runs during his college career and said that he'd like to add power as he matures, a trait that Senk believes is in the offing.
"Nick Tropeano was a fifth-rounder, and everyone was concerned about his velocity," said Senk. "Now he's probably pitching at 93-94 [mph], and I've heard he's even touched 96 or 97. The same thing is going to happen with Travis. He's an athletic kid, and he's only 20 years old. He's got a great body, and he's only going to get stronger through maturation. The power numbers are going to be there. He's an electric player with his speed, and as for the power, I'd bet a lot of money on that developing."
The annual Draft takes place this year on June 4-6, beginning with the first round and Comp Round A on Monday, June 4, at 7 p.m. ET. The first night of the event will be broadcast live on MLB Network and streamed live on MLB.com. Rounds 2-40 will also be streamed live on MLB.com, on June 5-6.
MLB.com's coverage, sponsored by CenturyLink, will include Draft Central, the Top 100 Draft Prospects list, Draft Tracker, a live interactive application that includes a searchable database of every Draft-eligible player, and Draft Caster. You can also keep up to date at Draft Central and by following @MLBDraft on Twitter. And get into the Draft conversation by tagging your tweets with #mlbdraft.
Spencer Fordin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.