We develop a unified, dynamical-systems narrative of the universe that traces a continuous chain of structure formation from the Big Bang to contemporary human societies and their artificial learning systems. Rather than treating cosmology, astrophysics, geophysics, biology, cognition, and machine intelligence as disjoint domains, we view each as successive regimes of dynamics on ever-richer state spaces, stitched together by phase transitions, symmetry-breaking events, and emergent attractors. Starting from inflationary field dynamics and the growth of primordial perturbations, we describe how gravitational instability sculpts the cosmic web, how dissipative collapse in baryonic matter yields stars and planets, and how planetary-scale geochemical cycles define long-lived nonequilibrium attractors. Within these attractors, we frame the origin of life as the emergence of self-maintaining reaction networks, evolutionary biology as flow on high-dimensional genotype-phenotype-environment manifolds, and brains as adaptive dynamical systems operating near critical surfaces. Human culture and technology-including modern machine learning and artificial intelligence-are then interpreted as symbolic and institutional dynamics that implement and refine engineered learning flows which recursively reshape their own phase space. Throughout, we emphasize recurring mathematical motifs-instability, bifurcation, multiscale coupling, and constrained flows on measure-zero subsets of the accessible state space. Our aim is not to present any new cosmological or biological model, but a cross-scale, theoretical perspective: a way of reading the universe's history as the evolution of dynamics itself, culminating (so far) in biological and artificial systems capable of modeling, predicting, and deliberately perturbing their own future trajectories.