Key point: Credence is the son of Kendra Dumbledore and Mustafa Kama.
I have, in my previous post(linked below), established Credence's birth year as 1898.
https://harrypotter.fandom.com/d/p/3343172654596354167
We know Credence is a Dumbledore but it's from his mother's side. He is the son of Mustafa Kama and Kendra Dumbledore.
Let's ponder over the timeline a bit:
1896- Mustafa's wife Laurena left him because of the imperius curse put by Corvus Lestrange Senior.
1897- Mustafa went to Godric's Hollow. I'm assuming he knew Kendra, perhaps he was her friend so went there when he was having an emotional breakdown.
Supporting this, ever wondered how Albus got in contact with Nicolas Flamel who lived in Paris? Well it indicates, the family had atleast some connections to Paris as well where Mustafa Kama used to live and thus Kendra's familiarity with him.
1898- Perhaps Kendra and Mustafa got intimate at certain point leading to Credence's birth this year.
But as we know, both Kendra and Mustafa were devoted to their spouse so they took this baby as a sign of disgrace for themselves. Mustafa left the baby and returned to Paris.
Kendra, therefore, gave this baby to Credence's aunt. All this was happening in absence of his sons who were busy at Hogwarts while Ariana was being looked after by Bathilda Bagshot. I'm taking Bathilda knew this secret.
Perhaps this act was the reason why Aunt Muriel described Kendra to be a terrible woman. She heard Bathilda saying these things when she was small and perhaps didn't entirely understand the topic. But might have taken up words like terrible or something.
1899- Credence's aunt visited Kendra who asked her to take the baby to America. Yes, she had afterall an American heritage, as the wiki notes and Harry too, so she would have sent the baby to someone she knew in America. During this visit, Ariana encountered the truth and got angry as how Kendra abandoned her brother. It resulted in a rage and the death of Kendra. But I suppose, she managed to obliviate Ariana before dying. I wonder, if this encounter transferred the Obscurus in Ariana(popular theory) to Credence.
1901- Credence's aunt took the ship to America.
I don't have lots of things to support these things but in future, I may try to find some more clues about this.