Optimization of indoor ventilation systems plays a crucial role in improving thermal comfort, air quality, and energy efficiency. However, ventilation optimization requires repeated evaluations of steady-state airflow under varying boundary conditions, where maintaining physical consistency across design iterations is essential. This requirement poses a fundamental challenge for surrogate-based optimization, as fast predictive models must remain faithful to the governing flow physics even for previously unseen configurations. In this study, we propose a physics-informed optimization framework for indoor airflow based on Physics-Informed Deep Operator Networks (PI-DeepONets). The network learns the nonlinear operator mapping boundary conditions to steady-state flow fields, enabling rapid evaluation while preserving consistency with the governing Navier-Stokes equations. By embedding the steady-state flow physics directly into the training process, the proposed approach maintains physical fidelity across varying boundary conditions without requiring retraining for each new configuration. As a first step toward three-dimensional ventilation optimization, we examine the feasibility of the proposed framework using a two-dimensional indoor airflow benchmark with variable inlet conditions. After training, the same PI-DeepONet model is used to predict steady-state velocity fields for different inlet configurations without retraining, and the predictions are assessed through comparison with CFD simulations. These preliminary results indicate that the proposed approach captures essential airflow responses to changes in ventilation conditions, providing a foundation for future integration into airflow optimization frameworks. The proposed physics-informed operator-learning framework is inherently extensible to three-dimensional configurations and coupled flow-thermal problems, including buoyancy effects.