This article challenges the dominant 'black box' metaphor in critical algorithm studies by proposing a phenomenological framework for understanding how social media algorithms manifest themselves in user experience. While the black box paradigm treats algorithms as opaque, self-contained entities that exist only 'behind the scenes', this article argues that algorithms are better understood as genetic phenomena that unfold temporally through user-platform interactions. Recent scholarship in critical algorithm studies has already identified various ways in which algorithms manifest in user experience: through affective responses, algorithmic self-reflexivity, disruptions of normal experience, points of contention, and folk theories. Yet, while these studies gesture toward a phenomenological understanding of algorithms, they do so without explicitly drawing on phenomenological theory. This article demonstrates how phenomenology, particularly a Husserlian genetic approach, can further conceptualize these already-documented algorithmic encounters. Moving beyond both the paradigm of artifacts and static phenomenological approaches, the analysis shows how algorithms emerge as inherently relational processes that co-constitute user experience over time. By reconceptualizing algorithms as genetic phenomena rather than black boxes, this paper provides a theoretical framework for understanding how algorithmic awareness develops from pre-reflective affective encounters to explicit folk theories, while remaining inextricably linked to users' self-understanding. This phenomenological framework contributes to a more nuanced understanding of algorithmic mediation in contemporary social media environments and opens new pathways for investigating digital technologies.