Autowiring in bundles is discouraged. However, I think you were on the right track, it's just that it seems you are confused about service ids. Keys in your services.yaml file are service IDs, not class names. It just happens that some of the service IDs equal their class names, which is not the case here. Have you tried

- App\Doctrine\CacheFactory:
  doctrine.orm.default_second_level_cache.default_cache_factory:
   class: App\Doctrine\CacheFactory:
   autowire: true
   autoconfigure: true

?

Thank you for the quick answer!

I have tried the suggestion above, and, while it works, it means that I have to define the factory based on this internal ID (which requires knowledge of how this bundle formats it in the first place).
Also to make your suggestion work, I have to remove the orm.entity_managers.default.second_level_cache.factory definition (it did not work with it in place and your suggestion).

@ostrolucky Sorry about the confusion, it looks like your suggestion does not work either, actually.

So:

services:
    doctrine.orm.default_second_level_cache.default_cache_factory:
        class: App\Doctrine\Caching\CacheFactory
        autowire: true
        autoconfigure: true

Does not work on its own, it just uses the DefaultCacheFactory implementation instead of my own.
If I specify the cache factory in the doctrine.yaml and keep the service declaration above, like so:

services:
    doctrine.orm.default_second_level_cache.default_cache_factory:
        class: App\Doctrine\Caching\CacheFactory
        autowire: true
        autoconfigure: true

doctrine:
    orm:
           entity_managers:
                  default:
                      second_level_cache:
                           enabled: true
                           factory: App\Doctrine\Caching\CacheFactory

I get an error when generating the cache:
Too few arguments to function App\Doctrine\Caching\CacheFactory::__construct(), 2 passed in /home/user/Projects/project/var/cache/dev/ContainerSnOQ4fQ/App_KernelDevDebugContainer.php on line 4646 and exactly 3 expected"

So, it seems the only viable option is the kernel pass.

doctrine.orm.entity_managers.*.second_level_cache.factory value at the moment represents a FQCN, not a service/service id. We use it to create new service. We could perhaps extend it to support service id too. PR welcome, but I think it can be tricky, because DoctrineExtension wouldn't know about app services.