There is a popular theory which claims that Shanks is the son of the captain of the Rocks Pirates, Rocks D. Xebec.
Some of the major points include the fact that the God Valley incident happened 38 years ago, and Shanks is 39 years old putting him around the age of one during the events of the clash between Roger, Garp and the Rocks Pirates.
The theory claims that Roger took in the infant Shanks to give him a life where he wouldn’t be killed off by the Marines for being the son of such an infamous pirate (this is why Roger entrusted Ace’s future to Garp becasue he knew that he wouldn’t allow a child to die for the crimes of their father). Shanks then proceeds to grow up in Roger’s crew and go on to become who he is today .
There is also another popular theory which talks about the interaction between Shanks and Whitebeard when Whitebeard says “The wound i got from that guy aches whenever I see your face” to Shanks implying that Shanks is somehow connected to the one who gave him the wound.
Since Whitebeard was in the crew of Xebec who is known for his iron fist and forcing his crew to join, and them constantly hurting eachother it’s not to that huge of an assumption to say Xebec may have been the one to injure Whitebeard therefore connecting Shanks to Xebec. This also gives reason for Shanks to be concerned about Blackbeard inheriting the will of Xebec.
Now that the fantastic chapter 967 has dropped I was going back and rereading Oden’s flashback chapters and then I noticed this panel in chapter 966.
This is pretty much confirmation that Roger and Rayleigh were taking care of a child at some point together. This is far before Ace was born, not that Roger took care of him anyway, and unless there is something I’ve missed (i.e. another Roger’s baby?) there hasn’t been any mention of a small child in the Roger Pirates crew at any point. The only conclusion I have come to is the good old days are referring to when the now 14-years-old Shanks was still just an innocent child and wasn’t causing trouble for the crew.
*Theory by Coal_AL