Who do you think the FBI would contract to do the work anyway 😬

Maybe not Google but it would sure be some private company. Our government doesn’t do stuff itself almost ever. It hires the private sector

Google isn't the only service checking for csam. Microsoft (and other file hosting services, likely) also have methods to do this. This doesn't mean they also host csam to detect it. I believe their checks use hash values to determine if a picture is already clocked as being in that category.

This has existed since 2009 and provides good insight on the topic, used for detecting all sorts of bad category images:

https://technologycoalition.org/news/the-tech-coalition-empowers-industry-to-combat-online-child-sexual-abuse-with-expanded-photodna-licensing/

Google wants to be able to recognize and remove it. They don't want the FBI all up in their business.