AbstractIn 2021, more than 80 million people worldwide will have been forced to flee their homes. Upon arrival in their new country, families may endure numerous hardships, yet succumbing to these challenges is not their single story. To understand how migrant‐background and refugee‐background children imagine more liveable futures beyond social and education barriers, financial stress and unresolved emotional issues, our study focuses on the stories that 8‐ to 10‐year‐old learners created while playing with building toys and stacking blocks in a Canadian elementary school. Drawing on the interconnected frameworks of story‐telling, identity, creative citizenship and play‐based pedagogies, our case study of 11 students illustrates that, in response to an invitation to support their real or imagined communities, learners engaged in literacy practices, built on their lived experiences and imagined strong identities to create stories of social responsibility and awareness, emphasising the human needs of securing food and fresh water, ensuring safety, and connecting and caring for the community. Our findings may encourage teachers to consider play‐based storytelling to address out‐of‐school social factors in their classrooms and to capitalise on students' inquiries to design interdisciplinary projects that can develop students' literacies and promote social activism.