Hope is an important emotion for fostering action regarding global warming (GW). This article’s experiment utilizes (a) a cognitive hope theory that combines agency and pathways-thinking and (b) prior (numerically driven inferencing) research on how estimating germane quantities, followed by surprising numeric feedback, impacts one’s beliefs and decision-making. We designed and assessed a short intervention that focally had 226 Americans estimate quantities regarding the impact/uptake of three GW solutions: sustainable (e.g., solar) electrification, energy efficiency (e.g., recycling), or reduced meat consumption. Changes in climate-change hope and GW beliefs represented the intervention’s effectiveness. (Nationalism, etc., were also assessed.) The intervention was generally successful—statistically significantly increasing participants’ (1) hope about humanity’s ability to tackle climate change and (2) GW acceptance/concern. Our results demonstrate climate-change hope’s close relationship with various constructs (particularly, acceptance of GW’s reality)—and that central facts can quickly modify such hope. We further replicated findings that core/surprising statistics can spawn environmental conceptual changes. Our results additionally support earlier-identified phenomena that people revise GW beliefs upon encountering salient, valid, surprising information. The findings (a) increase our laboratory’s (now 12) ways in which brief materials will boost GW acceptance/concern, and (b) imply that GW messaging should balance climate-dangers explications with hopeful solutions.