hum...
O. Kay.
I always thought Ace was very old. The Caesar coin, him mentioning Plato and an old japanese general. i always had the feeling Ace met them himself somehow and he was old enough to know the Roman Empire.

But straight saying he joined DGP on AD1. It's literally the birth year of Jesus and with all the "God" theme of the show + Ace being tied with thorns in the opening, I guess there's a theme.

Not saying Ace is literally Jesus Christ or even "God" himself (I don't expect Toei to go deep into that territory). But still. The choice of year is peculiar and can't be a coincidence.
But Ace being a martyr, suffering for other people in the world to be okay, is probably a thing.

Well, he definitely cannot be Christ, because he can`t joined the DGP at the age of 1 year) But the very fact that this date is mentioned, and not the fourth century of the Yayoi era, shows that the lore of the show is more Western-oriented. Is it necessary to look for the origin of Jamato in the history and myths of Ancient Rome? I guess we'll find out in time.
By the way, if I am not confusing anything, at about the same time, Tassel, together with the future Megido and the first Master of the Logos, found the Wonderful World according to Saber's lore. If there are still global crossovers planned in the franchise, you can show how Ace saves these five (or, more precisely, those who can be called into the project) from Jamato or other monsters in the past.

I say Ace is immortal. He's lived for many years and is searching for something while being tormented by the Grand Prix.

I think the apparent lack of curiosity on the part of the players is just the writers room playing for time until the show's first Big Reveal, which gives viewers time to try to work it out on their own.

At this point, I'll be very surprised if the people running the DGP aren't the people controlling the Jyamato. Why is DGP gamified rather than being a professional world-protecting organization? Why are the Riders' upgrades - and thus, their likelihood of successfully repelling the invaders - left to chance? Why aren't they selecting for players who know how to fight, rather than seemingly-random people off the street? Why are the players given incentive to compete instead of cooperate? Who is the intended audience for the Desire Grand Prix?

Sure, the DGP is apparently kept hidden from humanity, but who says humanity is the target audience?

Naturally, the answer to all these questions could simply come down to "Toei wanted the next Kamen Rider to ape Squid Game," but making the people who run the Desire Grant Prix the overall villains of the series (or at least their amoral enablers) would make for pretty good television. A structure that pivots away from the game toward defeating the Jyamato's overlords would also explain why our three-four core Riders are getting more character development than everyone else, since the series implies the DGP can have only one winner, and we're already to the final round. (I wouldn't be wholly surprised if Buffa gets eliminated; he's just less interesting than everyone else.) I can see maybe one more DGP happening, in which the players finally start asking the right questions, before the series pivots.

I could be entirely wrong, but even the images in the opening sequence suggest that the DGP isn't to be taken at face value.

I wonder whether Ace even has the option to quit playing, or if he's stuck because he's too popular with the audience.

In addition to the most obvious: "DGP organizers are villains" I have another version. In general, everything that the riders were told about the Jamato threat to humanity is true, but the DGP is not a real fight against them, but the preparation and selection of candidates. Hence the game color of everything that happens. Jamatos are artificial and weakened versions of the real ones.

But why then Ace is doing it over and over again?

I have three options for this:
a)He's not good enough to fight real Jamato. What better way to show the power of the show's villains than that the invincible Ace is not even worthy of fighting them?
b)He is actually an instructor training future fighters. Therefore, he simultaneously gives useful advice and punishes for excessive credulity.
c)He is indeed the best of the best, but he does not have the necessary moral qualities. Isn't it strange that all the bad guys in the show lost their rider qualifications while only the good guys died saving others (I'm not sure about Michinaga's friend, but he had that vibe too)? What if they did not die, but went to a real war with Jamato? And they chose them, because we need not the best fighters, but those who are ready to sacrifice themselves for the greater good. Let's say, because they will either die for sure, or simply will not be able to return, forever stuck in the world of Jamato.
In this case, Ace is not so bad that he loses his qualification, but he clearly cannot go any further because of his selfishness. Perhaps he is deliberately left in the game so that by his negative example he helps to identify people with good intentions, but weak will. Whoever remains true to the principles despite losing on points and heroically "dies" defending others - gets into a real war; who will try to take an example from him - it remains to play.
Again, in favor of this story is that the game rewards useful items for rescuing civilians and other players, and not for killing Jamato. According to this logic, the most likely contender will go to "real war with Jamato" - Keiwa, but he needs to bring his principles through actions, not just words.
But, if anything, I'm still more inclined towards the more obvious: "DGP villains." Still, the opening hints that the game and desires will be at the center of the plot, which contradicts this theory. Although, I remember, Blade and Hibiki had two openings...

No hard feelings of how the series handle it so far, and it's expected of kitsune-tanuki rivalry.

But it seems that, in general cool and capable characters are often given negative qualities, while the relatively more incompetent characters (naive, weak, etc.) are more often being made as the all-good one. This can portray as if only worse people can get the job done, while the goody ones can only rely on people around them, hopefully competent ones, softening up for their sake, or if not, constantly endure until that happens, which is honestly unreliable as hell. That also can be overdone to the point that some can conclude this in something like 'someone good can't be all powerful, someone powerful can't be all good' when it's not true/set in stone, just writing choices.

Then again, those asshole traits can be their main appeal of which development risks taking it away. Hypercompetent assholes can make for an ideal power fantasy that can make those seemingly critically acclaimed. And hypercompetent characters who aren't assholes has bigger chance to be bashed as "gary stus".

It depends if they'd keep him practically similar throughout the series looking from his predecessors, but a reminder that character development isn't only applicable to characters with serious negative qualities, albeit writing that is easier.

They made Agito with Overlord of Darkness.

Though otherwise, medias can and has employed 'messiah archetype' characters, when their role and story can use some of Christ references. There can be even a darker versions of that too and Ace likely gotta be that type considering what he did in this episode.

Well, we have an example of an invincible benevolent protagonist in Hibiki. Did the audience call him "gary stus"?

Hibiki is in a curious position. He's a teacher to Asumu, so he was portrayed as the person who can guide him down the right path. It makes sense they wanted to write him as competent and wise. He was old enough to have made his mistakes and learn from them before we met him.