Captain America is a likely candidate. He has a strong moral compass and a sense of protectiveness. He would see it as his duty to take care of the baby. His old - fashioned values would make him a great caregiver, like making sure the baby has a proper upbringing even in the middle of all the chaos in the Avenger's world.
One common plot could be the Avenger taking on a protective role over the baby. For example, they might keep the baby safe from villains who are after it for some special power the baby has. Maybe the baby is related to some important figure in the Avenger's world. Another plot could be the Avenger trying to find the baby's family while forming a bond with the baby during the search. They could face many challenges along the way, like dealing with other characters who misunderstand their intentions with the baby.
It could be Captain America. He has a strong sense of justice and kindness. So, if he found a dog, he would surely take it under his wing and protect it. Maybe he'd even train the dog to be a mascot for the Avengers.
The story could start with the Avenger having a bad day. They are feeling really down. Then they find a stray dog. At first, they're not sure what to do with it. But as they spend more time together, the dog's loyalty and unconditional love start to heal the Avenger's emotional wounds. Meanwhile, they also discover that the dog has a connection to an old enemy, which leads to a new adventure.
The baby could be an alien species that Goku has never encountered before. It might have special powers related to its alien origin, like the ability to control energy in a different way than Goku and his friends.
The baby could be an ordinary human baby that has some sort of latent magical ability that Raven senses. She then decides to protect the baby from the human world that may not understand or accept the baby's potential magic, and also from the magical world that might want to exploit the baby.
The baby could be an orphan from a nearby village that has been attacked. Kagome stumbles upon the baby while on her travels with Inuyasha. Since she has a big heart, she can't just leave the baby there, so she takes it with her.
The baby could be a lost elf child from a different part of the forest. Maybe their family was attacked by some dark force and Thranduil finds them by chance.
The baby could be a half - demon, related to some other important character in the series. Maybe it's the offspring of a character Sesshomaru has some history with.
One popular one is 'A Different Destiny' where Severus finding baby Harry sets off a chain of events that deviate from the original story's path. It has great character development.