The ubiquitous integration of technologies in organizations presents both opportunities and challenges for employees’ experiences of technostress and coping responses. Conventional Information Systems have long been recognized as sources of technostress, with most studies emphasizing technology characteristics as primary stressors. However, we argue that emerging technologies, such as Generative AI, can serve as coping tools as well. Drawing on Social Cognitive and Self-Discrepancy theories, we propose that while prompt engineering literacy may briefly lower self-efficacy (a J-curve effect) among non-experts, a supportive environment can smooth this learning curve. As prompt engineering literacy develops, self-efficacy rises, reducing self-discrepancies, mitigating technostress, and ultimately lowering job burnout. Practically, our framework offers guidance for organizations to enhance productivity through Generative AI deployment while supporting employee well-being.