The Penrose effect highlights managerial capacity as a limit to firm growth. Building on Penrose’s argument, this study explores the cognitive aspect of managerial capacity, specifically the constraint of managerial attention. The theoretical debate centers on whether narrow or broad attention better promotes firm growth. Narrow attention aids opportunity execution but risks overlooking critical blind spots, while broader attention enhances opportunity identification but can lead to cognitive overload. This study addresses the question: which approach is most beneficial for firm growth? Drawing from the attention-based view of the firm, we argue that opportunity identification plays a central role in firm growth and hypothesize a positive relationship between an executive’s breadth of strategic attention and firm growth. We examine internal factors (firm life cycle) and external factors (high-technology industry) as boundary conditions. We hypothesize that the positive relationship strengthens during the introduction, growth, and decline phases but weakens during the mature phase, and is stronger in high-technology sectors. We test these hypotheses using panel data from listed firms in the United States (30,205 firm-year observations of 4,944 firms) from 2010 to 2022 and find support for our predictions. Our findings contribute to the literature on the attention-based view of firm growth, situated attention, and the microfoundation of dynamic capabilities.