But despite the wide-eyed excitement at being a part of something they watched as kids, ultimately they came to these Games on a mission: to win a medal and hopefully gold.
With 18 holes to play, both players will have a shot at the ultimate prize.
Casey has been well-placed on the leaderboard from the off, starting out with a 67 and returning to the course early on Saturday morning to add a 68 after round two was disrupted due to poor weather.
He needed to keep his foot to the pedal when round three got underway soon after and the Englishman did just that.
Four birdies in his first seven holes took Casey into a share of the lead and despite a frustrating bogey-6 at the par-5 14th a pair of late birdies saw him card a 5-under 66.
That meant a rise of four spots to tied third, two behind leader Xander Schauffele.
Fleetwood had rather been treading water for the first two days, his nemesis the 18th hole. He double bogeyed it on Thursday to shoot 70 and bogeyed the last in a Friday 69.
The Southport golfer needed a low one on day three to have any hope of a medal and he got it: a superb 7-under 64 to vault him 15 spots to tied ninth.
There are some big names above him but Fleetwood will enter the final round just four off the lead. He's made more birdies (19) than anyone in the field through 54 holes and Olympic gold is still on the cards.
Justin Rose won gold for Great Britain in Rio in 2016 and now Casey and Fleetwood can repeat the feat in Tokyo.
"As I stand here right now I'm only thinking about one thing," said Casey after coming off the course.
Here's how the race for the gold stands after 54 holes:
Gold medal position
-14 Xander Schauffele
The American made his big move in round two thanks to an 8-under 63 - the joint-low lap so far - and kept out in front on Saturday with a third-round 68. He traded five birdies with two bogeys on day three, securing the solo lead with a closing birdie.
Schauffele has won some big events - the Tour Championship and the WGC-HSBC Champions - but he's not managed a victory since January 2019.
Looking at the stats, he ranks 4th for Strokes Gained: Approach and 7th for Strokes Gained: Putting. But he didn't find his first fairway until the 8th hole on Saturday.
Silver medal position
-13 Hideki Matsuyama
Being one of the faces of the Games, the home hero had huge pressure on his shoulders coming into the Olympics.
But Matsuyama's dreams of delivering gold are right on target after rounds of 69-64-67. He bogeyed the opening hole on Saturday but made five birdies from there to secure solo second and a place in the final group.
The Japanese golfer ranks 1st for SG: Around The Green and fourth for SG: Putting so is very much leaning on his short game. He's just 23rd (out of 60) for SG: Approach. After closing out victory in the Masters, can he do it again?
Bronze medal position
-12 Paul Casey, Carlos Ortiz
Birdies at 17 and 18 pulled Casey to within two and, perhaps crucially, he will play in the final three-ball alongside Schauffele and Matsuyama.
The Team GB star ranks 10th on Approach and 6th for SG: Putting. He's also 4th for Total Birdies.
Ortiz lost his place in the final group after a bogey at 18. He's still in a great position but there's a slight feeling he's just starting to drift after rounds of 65, 67, 69.
The concern for Ortiz is that he's 34th for Approach, recording a negative figure in round three. While ranking 2nd for SG: Putting, he also lost strokes to the field on the greens in round three.
-11 Sebastian Munoz, Rory McIlroy, Mito Pereira, Sepp Straka
-10 Tommy Fleetwood, Shane Lowry
-9 Abraham Ancer, Cameron Smith, Guido Migliozzi
Xander Schauffele quotes
"Golf is funny, you kind of have to fall back on parts of your game when other parts aren't working. I think I feel like yesterday I wouldn't say I was firing on all cylinders but things were clicking kind of coming home and, man, was it a different day today. So I'm going to try and get some better feels on the range.
"It's been a fun week, in a good position going into tomorrow."
Hideki Matsuyama quotes
"To be honest, the endurance part of my game has been struggling a little bit, but it's held up, thankfully it's held up the last few days, so it's going to hopefully hold up tomorrow as well.
"This is my first time playing the Olympics, so I'm not sure what to experience, but I'm sure it's going to be a great new experience and also not sure what kind of preparation I'll be able to put in before tomorrow's round, but I'm going to do my best.
"I played with Xander in the third and fourth day together at the Masters. I'm sure Xander will come out determined to win the gold medal tomorrow, so hopefully on my end too I'm going to come out strong on the mental side."
Paul Casey quotes
"Really good start. Really comfortable. I got another couple of birdies early. Made a great par save on 8 after burying it under the lip. I think they saw it on TV. But then after that just kind of went flat. Just couldn't get anything going. Went from sort of tied for the lead for about tied to sixth without doing a single thing.
"Then made a bogey on the par-5 (14), but then two great birdies on the last couple is what has got me back into things."
Rory McIlroy quotes
"I mean you go out on a Saturday, close to the lead and shoot 4-under, you've done your job, I guess. I got to 4-under after 13 and thought I could maybe squeeze an extra couple of shots out of the round, not birdieing 14 was disappointing, but then I bounced back well after the bogey on 16 with a birdie on 17 and yeah overall a good round of golf and it keeps me there in contention.
(On watching the leaderboard) "You don't want to look at it too much but I think this week it's like top three or nothing, right? So, yeah, you're taking peeks and glances at it and seeing how far off the pace you are. There's still 18 holes, a lot of golf still and a lot can happen. I need to go play a good round of golf tomorrow and see how it all unfolds."
Shane Lowry quotes
"It's nice to see a couple of medals been come back to Ireland. It would be nice to get a couple more. Myself and Rory have a great chance to do something. It would be great to see two of us on the podium.
"I think that's something that we obviously will talk about over dinner tonight and we'll go out tomorrow and give it our best. Like I said, it's a huge opportunity for me to do something very special for Irish golf and Irish sport I think."
Tommy Fleetwood quotes
"I've been struggling for momentum a lot recently, like I feel like my game has been coming back and it's just about getting those good rounds under your belt. That's the lowest round I've had for a very long time, really. It was just nice.
"Just got on a run and that was great and it was nice to come down the stretch feeling like constantly giving myself chances and moving up the board. We all know what places matter this week, so it's nice to actually be within touching distance."