Whitebeard refers to Oden as "little brother" and between the two there are 15 years of difference.
Big Mom refers to Kaido as "little brother".
Possible hint about Kaido's age?
What if there are 15 years of difference between this two as well? Then Kaido would be 53 currently (since BM is 68).
This would be consistent with Sengoku's description of Kaido as "just an apprentice", as in this way Kaido would have been 15 years old at the time of God Valley incident, just like Buggy and Shanks were 15 (apprentices) in their last year on Roger's ship.