Interesting pick here after some analizing as I believe Stefanos really has a decent chance reaching a final here and the odds for the gold medal are better than tempting. Let's try to break it down :)
The greek will kick off his campaign today vs Bergs who can be a tricky player but nothing Tsitsipas can not handle. He's been underperforming for the most part of the season, but when it comes to clay, he is a different type of beast. Although made a but quicker for the Olympics, the courts at French Open are very well known to Stefanos as he made his best slam result here reaching (and ultimately choking) finals in '21 against Djokovic.
The Olympics will be played in 2 best out.of 3 which I consider to be better for him as there are several players in this tournament who prefer playing in best out of 5 on big events and one is in his draw. Although 37 years of age, but still. Speaking of his draw, let's take a look on his potential rivals and his projected road to the final.
ROUND 1
It should be a routine opening for Stef as he faces a player he beat 2x already (once this year at AO). Zizou can be a tricky player, sometimes, but he's no match for the Greek on clay.
ROUND 2
He will face the winner of Echargui - Evans (probably Evans) in the second round. I see no potential problems for him there. Leads 4-0 against the Brit who really has nothing to offer on clay courts with his backhand slice.
ROUND 3
The third round most likely brings Sebastian Baez who is playing really bad in this moment (having weak displays both in Hamburg and Kitzbuhl. Tsitsipas has 2-0 in H2H against the argentinian and is better than him almost in every segment, except for backhand cross court exanges. But he has enough weapons to make that problem go away in the first place.
ROUND 5 (Quarter Finals)
Now things get tricky. If we assume Djokovic is fit, he is most likely Stef's rival here as I don't see Nadal progressing against Djokovic (or even Fuscovic for that matter). Raonic is no way near competitive player here, Arnaldi and Fuscovic are a level below currently. A dark horse can be Arthur Fils who will have home support and is on the roll winning Hamburg, but he'll face Novak in the previous round if he get's through. So let's just 'pretend' Tsitsipas plays Djokovic in QF. Dreadfull H2H of 2-11 against the Serb, however, giving the recent developing around Novak and his knee, I would give Stefanos a very decent shot. Djokovic played Wimbley final (got a bit lucky with the draw as well), however the question remains. What makes him even more dangerous is that these games will be his last and he only needs this trophy basicaly to seal his collection and the question on to who is the G.O.A.T. Thus he is the favourite no 2, right behind Carlos. But as said before, Novak's fitness along with the fact it's not played in best out of 3 and on clay, gives Tsitsipas something to hope for. He proved he can play against Novak who is 100% fit already.
ROUND 6 (Semi Finals)
If Stefanos beats Djokovic, I very much doubt he will not be able to beat anybody from the second quarter and that will be most likely Zverev. With all due respect to others, there are only 2 names here that can face Sasha in QF (Fritz and Musetti). Fritz and clay, well, that's a done deal. Musetti would present a threat if he didn't decide to go deep in Umag and he actually plays final today vs Cerundolo, which says to me he didn't prioritize this OG. And aill face tricky Monfils in R2 tomorrow. So let's assume Zverev as most logical choice to be Stef's rival in SF. Tsitsipas has 10-5 in H2H and 4-1 on clay, proving to be a tough nut for Zverev who comes here as the defending champion (only Murray defended the title) and with questionable fitness regarding his knee. Although he looked okay-ish in Hamburg, it can pop up anytime.
The only issue I see here for the Greek is Novak Djokovic. If he manages to overcome that he is in the Final in my opinion, since his road to QF seems really light on paper.
FINAL
In the finals he will probably encounter Alcaraz again who beat him in RG this year and who is favourite no 1 to take gold. Either way, at this point, cash out also becomes an option although I believe Tsitsipas would put much more resistance and be competitive, especialy because he has 0-6 against him and made his mission to beat him (it was the same with Medvedev).
Overall at @29, Tsitsipas deserves a fair shot giving all factors given. Let's see :)