While infrastructures of media and of migration currently converge in specific ways, in this commentary, we consider how these infrastructures always reflect distinctive moments in media history, as well as in migration history. An archaeological approach to infrastructure posits that media infrastructures do not spring into action fully formed, and neither is there ever a moment when they would be fully formed. We propose the perspective of deep time of infrastructures as a way of opening up unresolved questions about what critical researchers can and should do with historically-informed inquiry of media technologies across migration contexts. We specifically operationalize the deep time of media and migration infrastructures by addressing the three dimensions of: (1) materialities; (2) practices; and (3) imaginaries.