Is it possible to 'pass providers' from view components to content components?

I am facing this issue over and over and cannot find neither the solution, nor the information (docs) that is not possible by design.

If I have a component in template, it can be injected in constructor of child component (this is of course working):

@Component({
  selector: 'aaa',
  template: '<div>This is AAA {{prop}}><div><ng-content></ng-content></div>'
})
export class AComponent {
  prop = Math.random();
}

@Component({
  selector: 'bbb',
  template: '<div>This is BBB. Parent is AAA {{a.prop}}</div>'
})
export class BComponent {
  constructor(public a: AComponent) { }
}

<aaa><bbb></bbb></aaa>

Result:

This is AAA 0.4997284193879621>
This is BBB. Parent is AAA 0.4997284193879621

But is it possible to achieve this if the component that I want to inject, is part of other component's view?

This scenario does not work:

@Component({
  selector: 'ccc',
  template: '<aaa><ng-content></ng-content></aaa>'
})
export class CComponent {
}

<ccc><bbb></bbb></ccc>

Ends up with NullInjectorError: R3InjectorError(AppModule)[AComponent -> AComponent -> AComponent]: NullInjectorError: No provider for AComponent!

Is there a way to write such a provider (or viewProvider) in CComponent, that would provide injectable objects from it's template/view?