TL;DR: It is not possible to put together a consistent biography of Poirot that includes all the stories.
Precise dates are very rare in the Poirot corpus, and there are few references to historical events that can be used to give a terminus post quem, but here is a selection of significant dates.
“I had a bad failure in Belgium in 1893. You recollect, Hastings? I recounted it to you. The affair of the box of chocolates.”
Agatha Christie (1932). Peril at End House, chapter 15. London: Collins.
In the story itself Poirot says, “At that time, mon ami, I was, as you know, a member of the Belgian detective force” but as to the date he is vague:
“It was at the time of the terrible struggle in France between church and state.”
Agatha Christie (1923). ‘The Clue of the Chocolate Box’. The Sketch, issue 1582. Reprinted in Poirot’s Early Cases.
This places the story during the conflict over state secularism that occupied the last quarter of the 19th century and culminated in the Loi du 9 décembre 1905.
However, in Cards on the Table Poirot says that his last failure was “twenty-eight years ago”:
“Don't you ever have a failure, Monsieur Poirot?"
“The last time was twenty-eight years ago,” said Poirot with dignity. “And even then, there were circumstances—but no matter.”
Agatha Christie (1936). Cards on the Table, chapter 15. London: Collins.
When does Cards on the Table take place? It must post-date The A.B.C. Murders, since Miss Meredith says:
“I know all about you, Monsieur Poirot. It was you who really solved the A.B.C. crimes.”
Cards on the Table, chapter 2.
And The A.B.C. Murders is set in 1935:
It was in June of 1935 that I came home from my ranch in South America for a stay of about six months.
Agatha Christie (1936). The ABC Murders, chapter 1. London: Collins.
So Poirot’s “twenty-eight years ago” can be no earlier than 1907. This suggests that he had more than one failure, so that his “last failure” is not the same case as ‘The Clue of the Chocolate Box’.
[Inspector Japp] turned to the other man. “You’ve heard me speak of Mr. Poirot? It was in 1904 he and I worked together—the Abercrombie forgery case—you remember, he was run down in Brussels. Ah, those were great days, moosier. Then, do you remember ‘Baron’ Altara? There was a pretty rogue for you! He eluded the clutches of half the police in Europe. But we nailed him in Antwerp—thanks to Mr. Poirot here.”
Agatha Christie (1920). The Mysterious Affair at Styles, chapter 7. London: Bodley Head.
In Three Act Tragedy, Poirot says that he was “due to retire” from the Belgian police on the eve of the First World War:
“See you, as a boy I was poor. There were many of us. We had to get on in the world. I entered the Police Force. I worked hard. Slowly I rose in that Force. I began to make a name for myself. I made a name for myself. I began to acquire an international reputation. At last, I was due to retire. There came the War. I was injured. I came, a sad and weary refugee, to England.”
Agatha Christie (1934). Three Act Tragedy, chapter 6. London: Collins.
The Mysterious Affair at Styles is not precisely dated, but it is set during the First World War. Captain Arthur Hastings has been “invalided home from the Front”, Mary Cavendish is a Land Girl, Cynthia Murdoch is a pharmacist in the Voluntary Aid Detachment, Mrs Inglethorp says, “We are quite a war household; nothing is wasted here”, and there are Belgian refugees in the village. Some time around 1916 seems to be indicated, and this date is confirmed by Hastings in Curtain:
Ah! If I could go back—live life all over again. If this could have been that day in 1916 when I first travelled to Styles…
Agatha Christie (1975). Curtain: Poirot’s Last Case, chapter 1. London: Collins.
Curtain is set during or after the Second World War, according to Hastings:
How long ago was it that I had taken this self-same journey? Had felt (ridiculously) that the best of life was over for me! Wounded in that war that for me would always be the war—the war that was wiped out now by a second and a more desperate war.
Curtain, chapter 1.
A remark from Poirot suggests that the war is ongoing or only recently concluded, otherwise “the last war” would be the Second World War, not the First:
“Like your Mr Asquith in the last war.”
Curtain, chapter 8.
Hastings meets “an old woman with rheumy eyes and an unpleasantly ghoulish manner” who describes the passage of time since the earlier novel:
“Twenty years ago and over. When the old lady died up at the Court. That was the first murder we had to Styles. Won’t be the last, I say. Old Mrs Inglethorp, her husband done her in, so we all said. Sure of it, we was.”
Curtain, chapter 15.
This would seem to place Curtain in the mid-1940s: indeed, by 1946, it would already be thirty years since Mrs Inglethorp’s murder.
Hallowe’en Party is set after the suspension of capital punishment for murder in 1965:
Faint memories flashed across his mind. Rather a celebrated case, more celebrated actually than it had showed any signs of being, a case that had seemed cut and dried. Of course! It came to him that his nephew Robert had been connected with it, had been Junior Counsel. A psychopathic killer, it had seemed, a man who had hardly bothered to try and defend himself, a man whom you might have thought really wanted to be hanged (because it had meant hanging at that time). No fifteen years, or indefinite number of years in prison. No. You paid the full penalty and more’s the pity they’ve given it up, so Mr Fullerton thought in his dry mind.
Agatha Christie (1969). Hallowe’en Party, chapter 12. London: Collins.
(This paragraph references the events of Mrs McGinty’s Dead, 1952.)
Elephants Can Remember is set in the early 1970s:
“A speech!” Mrs. Oliver sounded horrified. “No, of course not. You know I never make speeches.”
“Well, I thought they always did at these here literary luncheons. That’s what you’re going to, isn’t it? Famous writers of nineteen seventy-three—or wherever year it is we’ve got to now.”
Agatha Christie (1972). Elephants Can Remember, chapter 1. London: Collins.
“What I want," said Mrs. Oliver with firmness and the determination of a spoiled child, "is my nineteen seventy address book. And I think nineteen sixty-nine as well. Please look for it as quick as you can, will you?”
Elephants Can Remember, chapter 3.
Since Curtain is ‘Poirot’s Last Case’ and so would have to follow Hallowe’en Party and Elephants Can Remember in any coherent biography, the only way to make the chronology consistent would be to imagine that the characters are mistaken or lying or joking in some or all of these works. But I think that’s a sign that such an exercise would be futile.
Christie was well aware of this. She satirizes the difficulty of having such a long-running series detective in Mrs McGinty’s Dead, where crime novelist Ariadne Oliver and playwright Robin Upwood are collaborating on a play in which Oliver’s Finnish detective, Sven Hjerson, is to be the hero:
Robin continued blithely: “What I feel is, here’s that wonderful young man, parachuted down—”
Mrs Oliver interrupted: “He’s sixty.”
“I don’t see him like that. Thirty-five—not a day older.”
“But I’ve been writing books about him for thirty years, and he was at least thirty-five in the first one.”
“But, darling, if he’s sixty, you can’t have the tension between him and the girl—what’s her name? Ingrid. I mean, it would make him just a nasty old man!”
“It certainly would.”
Agatha Christie (1952). Mrs McGinty’s Dead, chapter 12. London: Collins.
However, nothing in Christie’s oeuvre suggests that she was all that bothered by series consistency. While they may share characters, each novel and story stands on its own. There are occasional references to other stories but these are never important to the plot. It’s not just Poirot’s age that varies: for example, Hastings is about to marry Dulcie Duveen at the conclusion of The Murder on the Links (1923) but in Peril at End House (1932) he calls his wife ‘Bella’, the name of Dulcie’s twin sister in the earlier novel.