Pass config data using forRoot

You are almost there, simply provide both SampleService and config in your module like below:

export class SampleModule {
  static forRoot(config: CustomConfig): ModuleWithProviders<SampleModule> {
    // User config get logged here
    console.log(config);
    return {
      ngModule: SampleModule,
      providers: [SampleService, {provide: 'config', useValue: config}]
    };
  }
}

@Injectable()
export class SampleService {

  foo: string;

  constructor(@Inject('config') private config:CustomConfig) {
    this.foo = ThirdParyAPI( config );
  }
}

Update:

Since Angular 7 ModuleWithProviders is generic, so it needs ModuleWithProviders<SampleService>