Test-time prompt tuning (TPT) has emerged as a promising technique for enhancing the adaptability of vision-language models by optimizing textual prompts using unlabeled test data. However, prior studies have observed that TPT often produces poorly calibrated models, raising concerns about the reliability of their predictions. Recent works address this issue by incorporating additional regularization terms that constrain model outputs, which improve calibration but often degrade performance. In this work, we reveal that these regularization strategies implicitly encourage optimization toward flatter minima, and that the sharpness of the loss landscape around adapted prompts is a key factor governing calibration quality. Motivated by this observation, we introduce Flatness-aware Prompt Pretraining (FPP), a simple yet effective pretraining framework for TPT that initializes prompts within flatter regions of the loss landscape prior to adaptation. We show that simply replacing the initialization in existing TPT pipelines--without modifying any other components--is sufficient to improve both calibration and performance. Notably, FPP requires no labeled data and incurs no additional computational costs during test-time tuning, making it highly practical for real-world deployment. The code is available at: https://github.com/YonseiML/fpp.