With the continuous rise in the popularity of Android mobile devices, automated testing of apps has become more important than ever. Android apps are event-driven programs. Unfortunately, generating all possible types of events by interacting with the app's interface is challenging for an automated testing approach. Callback-driven testing eliminates the need for event generation by directly invoking app callbacks. However, existing callback-driven testing techniques assume prior knowledge of Android callbacks, and they rely on a human expert, who is familiar with the Android API, to write stub code that prepares callback arguments before invocation. Since the Android API is huge and keeps evolving, prior techniques could only support a small fraction of callbacks present in the Android framework. In this work, we introduce Columbus, a callback-driven testing technique that employs two strategies to eliminate the need for human involvement: (i) it automatically identifies callbacks by simultaneously analyzing both the Android framework and the app under test, and (ii) it uses a combination of under-constrained symbolic execution (primitive arguments), and type-guided dynamic heap introspection (object arguments) to generate valid and effective inputs. Lastly, Columbus integrates two novel feedback mechanisms -- data dependency and crash-guidance, during testing to increase the likelihood of triggering crashes, and maximizing coverage. In our evaluation, Columbus outperforms state-of-the-art model-driven, checkpoint-based, and callback-driven testing tools both in terms of crashes and coverage.