In 2016, the Pioneering Punjabi Digital Archive (PPDA) went online. Attempting to reveal how the Punjabi community struggled and then thrived in California, the PPDA accumulates narratives of Punjabi American life. Against such models of archival intimacy and recovery, which look to cultivate limitless public access to a knowable and transparent subject while reducing structural precarity to the failure of an exceptional Punjabi, this article hesitates in a vexed archival space without guarantees. Within this hesitation, it explores the traces of untimely lives displaced in creating archival legibility—traces that reveal a different form of being that challenge the additive logic of the PPDA. This hesitation is cultivated through a comparative approach that couples archival and ethnographic research based on articles about Punjabi American life in both the archive and public sphere alongside ethnographic work conducted with Sikh immigrants who work in canneries and the fields. The aim is to pause in the present impasse to consider the nonbecoming of unknown forms—an ethnographic “reaching and ungrasping” in which the future is not fixed as a requirement for thinking, refusing the accumulating demands of narrative sequence that archiving presents.