Kakuzu. He's all about money and assets. If he thought that rescuing the female OC could lead to some sort of financial gain, he'd be the one to start the rescue. Maybe she has information about a rich bounty or a hidden cache of valuable ninja tools.
Deidara. He might be attracted to the female OC's unique appearance or abilities. He loves things that are 'artistic' in his eyes. If he saw the OC as some sort of living art or a potential source of inspiration, he could be the one to initiate the rescue, regardless of what the other Akatsuki members think.
Itachi. He's one of the more complex and morally gray members of the Akatsuki. If he saw that the female OC was in a situation that could potentially cause chaos or harm to the ninja world in a larger sense, he might initiate the rescue. He's also the type who might see some value in the OC that others don't.
Itachi could be a likely candidate. He has always had a complex relationship with Naruto. He knows Naruto's potential and his importance in Sasuke's life. Itachi might see Naruto as a key to changing the Akatsuki from within. He could approach Naruto with his calm and mysterious demeanor, explaining to him the real goals of the Akatsuki that are hidden beneath their violent exterior.
Pain would still be a likely candidate. His Rinnegan gives him a powerful and commanding presence. He has the ability to see the big picture and make strategic decisions for the group.
Well, it could be that the female OC is in danger from some other ninja group. The Akatsuki, known for their power, decides to rescue her for their own purposes, like using her unique abilities. Maybe she has some special knowledge about a powerful jutsu or a hidden treasure. And they rescue her from a dangerous place, like a fortress full of enemy ninjas.
I think Hidan would be the most difficult. He was always so hot - headed as an adult. As a baby, he would probably be very fussy and hard to calm down. He might throw tantrums all the time and not listen to whoever is taking care of him.
Itachi. He has his own moral code and he might see something in Chibi Sakura that reminds him of his own will to protect. He could form an alliance with her if he believes it would be for the greater good, like stopping the more extreme members of Akatsuki from causing too much destruction.
Itachi could be the most challenging. He's not only extremely powerful with his Sharingan and genjutsu skills, but he's also very intelligent. He could outwit Naruto in battle and has the ability to use Amaterasu, which is a very dangerous jutsu. Naruto would have to be on top of his game both mentally and physically to defeat him.
Power - seeking is also prevalent. The oc may join the Akatsuki to gain more power, either to achieve a personal goal or to be part of a powerful organization. They might be on a quest to master a particular jutsu that only the Akatsuki can offer access to.
Itachi and Kisame could be a pair with a close bond. Itachi is a very reserved person, but Kisame seems to respect and understand him to some extent. They often work together on missions, and this could be seen as a form of 'family' bond within the Akatsuki. Another possibility is Deidara and Sasori. Despite their differences in art forms, they seem to have a connection. Deidara looks up to Sasori in some ways, like a younger brother might look up to an older one.
Definitely Itachi. He has a complex character and his own sense of justice. He might see Naruto as a key to changing the shinobi world in a different way than what the Akatsuki originally planned. Another one could be Kisame. He is loyal to Itachi and would likely follow Itachi's lead in taking care of Naruto.
Pein could be another one. As the leader of the Akatsuki, he might see baby Naruto as a means to an end. He could either want to use Naruto for his own grand plans or, in a more interesting twist, be swayed by Naruto's innocence and change his perspective on the Akatsuki's goals.