How can Credence be Dumbledore's brother?

As mentioned by Paulie_D in his comment or the respective answer from sister site it seems not to be a possibility for now but never say never as there suppose to be three more sequels planned to turn the tables, also to be remember Grindelwald is not that trustworthy narrator either.

Digital Spy also tried to dig into all the possibility to make it logical with dead ends:

Credence's date of birth

In the first Fantastic Beasts movie, Credence is still living with his adopted mother and Ezra Miller, who plays him, once reportedly said that Credence was 18 years old in an interview.

But let's be generous, say Ezra was mistaken, and assume Credence was actually in his twenties. If Credence and Albus share the same mother, this is still pretty much implausible.

In Harry Potter and the Deathly Hallows, it is revealed that Albus' mother Kendra was killed by his little sister, Ariana, in 1899. Had Kendra given birth to the baby none of us had ever heard of before her death, that means that Credence would be 28 years of age at the very least during the events of Fantastic Beasts, which is set in 1926.

What's more, since Leta and Newt were born in 1897, this means that they would have been just two years older than Credence if he was born before Kendra's death.

But what if Credence was born after Kendra's supposed death date? Harry Potter's Wiki lists Credence as being born in 1901, the same year as the boat journey to New York, which of course means that in all likelihood Kendra is NOT Aurelius' mother.

The only way that this could be plausible is if she faked her death then had baby Aurelius two years later. But Kendra had a troubled daughter that she never would have left, especially after spending years fiercely protecting her, and was even buried with her child in Godric's Hollow.

What if Aurelius shared the same father as Albus instead?

The alternative suggestion would be that Albus' father Percival had another child with someone else, years after Kendra's death. It is also fairly impossible since Percival is known to have died in Azkaban after being imprisoned there in 1891.

Even if we were to suggest that he escaped the prison, this is incredibly unlikely for two reasons. Firstly, Sirius was famously the first prisoner who ever knowingly escaped Azkaban and, secondly, the only other person to escape was Barty Crouch Jr, who swapped places with his mother using Polyjuice Potion.

It is also strongly implicated that Credence's adoptive mother, Mary Lou Barebone, knew something about Credence's birth mother, calling her a "wicked, unnatural woman" in the first Fantastic Beasts installment.

The life and lies of the Dumbledore family

Another reason that the huge revelation makes very little sense is that a fourth Dumbledore sibling isn't even alluded to in the Harry Potter series. Of course, this would all make sense if Albus and Aberforth didn't have a clue that they had a second brother since we hear all about the family's history from their perspectives.

However, The Crimes of Grindelwald seems to insinuate that Albus – and indeed his old friend Grindelwald – were well aware of Credence's heritage, so much so that the plot of the sequel centers on the pair trying to bring Credence to their side before the other one gets a chance.

So why on earth did this never come up when Dumbledore is an old man in the Harry Potter series? Why did Rita Skeeter not even uncover it for her tell-all book? Why did Aberforth neglect to mention a younger brother while filling in Harry, Ron, and Hermione on his family's history?

Aurelius also isn't included when JK Rowling revealed what Dumbledore saw when looking into the Mirror of Erised, although every other family member is. Speaking on a Leaky Cauldron web chat, she said: "[Albus] saw his family alive, whole and happy – Ariana, Percival and Kendra all returned to him, and Aberforth reconciled to him."

Since the film strongly hints that Credence really is a Dumbledore, why doesn't Albus see him as a true member of his family? Could Grindelwald be lying and somehow have planted the phoenix that confirmed Credence's true identity? What is the truth?!

So, in short, it makes no sense, for now, all hypothesis are going dead end. So it's either Grindelwald is lying or soemthing esle is going on we didn't know before.

With Fantastic Beasts: The Secrets of Dumbledore (2022), we now know that Credence is

the son of Albus' brother, Aberforth

Dumbledore's sister had a shadow inside her because she could not use magic. When she died the shadow maybe moved to Credence. That is how Credence got Dumbledore's soul so the phoenix appeared before him.

But I think everything is possible. Maybe Ariana was alive. After all, this is Fantastic Beasts. It's magic. So everything is possible.