Poirot's Early History and Rise to Fame
I was working on this as part of a reply to someone else and decided the rest of the sub might appreciate this.
Canonically, Poirot was not always a famous detective. In Christie's first book, The Mysterious Affair at Styles, Poirot is virtually unknown in the UK. It is his success in the highly-publicized Styles case that puts him on the map and launches his career as a private eye. Since Poirot's career (very roughly) follows real-time, he was not famous in the UK until Styles, which occurred circa 1917.
We learn in Styles that before the Great War, Poirot has been a well-respected and high-ranking officer in the Belgian police force, eventually becoming its chief. But when the Great War broke out, Poirot joined the resistance. He was injured and escaped to the UK, likely circa 1916. He came to Styles due to the philanthropy of Mrs. Inglethorpe. In a highly insular Britain at the time, regardless of his successes in Belgium, he would've been mostly known as "just another Belgie," if he wasn't being mistaken for a "frog." We don't know exactly how long Poirot was at Styles before Mrs. Inglethorpe is murdered, but we know the events of the novel take place around the height of the war.
One of the only people in the UK who knew of Poirot's success in Belgium and his intellectual prowess was then-Detective Inspector Japp (promoted later to Chief Inspector). In Styles, Japp speaks very highly of Poirot, referencing a case where a wanted criminal had eluded police all over Europe. "But we caught him in Antwerp--thanks to Mr. Poirot here."
Poirot did not become a celebrated private detective until after the resolution of the Styles case, but his fame came extremely quickly. Chronologically, his next mystery is The Murder on the Links, which takes place in France and has (I believe) contains no particular references to his fame, although he is summoned there by a client, so we know he's a private eye and taking cases. But his next set of adventures are told in the Poirot Investigates series of short stories.
In the first of these, The Adventure of the Western Star, Poirot refers to himself as a "fashionable detective" as he is being sought out by a famous American film star. Over the course of the collection, Poirot will investigate mysteries of varying degrees of noteriety. But it's clear that right from the very beginning and as a result of the Styles affair, Poirot has catapulted to becoming one of the UK's most renown private detectives.
Over the course of Poirot Investigates, he solves numerous high-profile crimes such as The Million Dollar Bond Robbery and The Disappearance of Mr. Davenheim. He also solves cases that, while not of public noteriety, give him a substantial reputation with Scotland Yard, such as with The Adventure of the Cheap Flat and, in perhaps one of the most significant cases of his entire career, The Kidnapped Prime Minister.
At the beginning of one of these significant cases, The Jewel Robbery at the Grand Metropolitan, Hastings discusses just how famous and sought-after Poirot has become, stating that Poirot had become an extremely prolific work horse, due in part to his "Flemish thrift," but also because he desired to take on lesser-known cases that simply interested him. This all culminates in Poirot's involvement in The Big Four.
Therefore, based on what we know from publication history, therefore Poirot was an extremely renown and fashionable detective between (approximately) 1917 and 1926. He then famously enters retirement to grow vegetable marrows, but is catapulted back into fame with The Murder of Roger Ackroyd. This is the first time, I believe, in which Poirot is described as a "has-been," a "mountebank," or "gaga." Bearing in mind that Poirot was already "elderly" in 1917 (being charitable, he was in his at youngest in his early 50's), he is likely nearly 70 by the events of Peril at End House in 1932.
The majority of Poirot cases that we're familiar with, then, take place during the twilight of his career. If time scaled perfectly with real life, Poirot would be about 100 during the events of Curtain. Christie herself talked about the difficulty of having made her sleuth already elderly at the beginning, and so it's likely that, unlike Tommy and Tuppence who do seem to scale perfectly with real life, Poirot ages a little bit slower.
As a sidenote, if we MUST have new canonical Poirot stories, I would really like to see them set in the early twenties during the pinnacle of his career with Hastings as his sidekick. An author could write nearly anything during that time period and it could potentially make sense, given the amount of work and the scale of the mysteries that Poirot solved in that period.
I hope y'all find that interesting, and feel free to double check me on various things. I did a little bit of research on this but I'm going off my memory for the content of some of the stories.