This study casts light on two online learning initiatives funded by the European Commission, and queries their role as policy actors in the long-term project of a "borderless" European Education Area and/or in the remediation of the so-called "refugee crisis." Particularly, the study aims to contribute to existing research on the policy enactment of European education spaces, while also addressing their implicated times. Social topology has guided a theoretical-conceptual focus on bordering practices, socio-technological architectures, and user interfaces, and their enactment of forms of Europe. This informed the methodology to center around "active navigations" on user interfaces of these online learning initiatives, based on the argument that these concretize bordering practices and forms of spaces-times. The findings, presented as re-constructions of the active navigations, stress multiple possibilities EC-funded online learning initiatives to evolve, including shifting responsibilities and differentiated learning trajectories. By highlighting these possibilities, the study aims to interpose the relatively short development of digitalization in (European) education, in which digital technologies have been positioned as "flexible" solutions in times of crisis. The study thereby stirs up discussions on how European online learning initiatives could integrate long-term visions with crisis remediations and, accordingly, could support continuously renewable educational spaces-times.