Institutions play a critical role in enabling communities to manage common-pool resources and avert tragedies of the commons. Prior research suggests institutions emerge when universal participation yields greater collective benefits than non-cooperation. However, a fundamental issue arises: individuals typically perceive participation as advantageous only after an institution is established, creating a paradox—how can institutions form if no one will join before a critical mass exists? We term this conundrum the institution bootstrapping problem and propose that misperception—specifically, agents’ erroneous belief that an institution already exists—could resolve this paradox. By integrating well-documented psychological phenomena—including cognitive biases and perceptual noise—into a game-theoretic framework, we demonstrate how these factors collectively mitigate the bootstrapping problem. Notably, unbiased perceptual noise (e.g., noise arising from agents’ differing heterogeneous physical or social contexts) drastically reduces the critical mass of cooperators required for institutional emergence. This effect intensifies with greater diversity of perceptions, suggesting that variability among agents perceptions facilitates collective action. We explain this counter-intuitive result through asymmetric boundary conditions: proportional underestimation of low-probability sanctions produces distinct outcomes compared to equivalent overestimation. Furthermore, the type of perceptual distortion—proportional versus absolute yields qualitatively different evolutionary pathways. These findings challenge conventional assumptions about rationality in institutional design, highlighting how “noisy” cognition can paradoxically enhance cooperation. Our analysis highlights how, even though biases and uncertainty are often perceived as defects of human cognition, they create the cognitive conditions that enable institutions to bootstrap into existence.