This article examines institutional exclusions of refugee pupils in German state schools within the context of changing European migration and education policies following Russia’s invasion of Ukraine. Drawing on concepts of critical time studies and guided interviews with teachers, principals and social workers, we explore how ‘uncertain futures’ of refugee pupils are constructed and addressed within institutional ‘timescapes’ and how these practices might (re)produce (differentiated) forms of exclusion. Despite changes at EU level towards recognising biographical uncertainty, our findings reveal that schools continue to pressure pupils to transform uncertain futures into certain futures. By requiring pupils to adapt rapidly to the institutional timescape, schools impose on them a logic of ‘acceleration’ interwoven with a unilinear notion of ‘rapid integration’ that denies the individual pace of arrival processes. These institutionalised temporal expectations (re)produce distinctions between different groups of newcomers, which serve to justify (partial) exclusions in the German school system. While some school professionals challenge the dominant timescape, ‘practices of resistance’ remain fragile as they can easily be discredited.