We propose and analyze two distinct routes toward realizing interacting symmetry-protected topological (SPT) phases via periodic driving. First, we demonstrate that a driven transversefield Ising model can be used to engineer complex interactions which enable the emulation of an equilibrium SPT phase. This phase remains stable only within a parametric time scale controlled by the driving frequency, beyond which its topological features break down. To overcome this issue, we consider an alternate route based upon realizing an intrinsically Floquet SPT phase that does not have any equilibrium analog. In both cases, we show that disorder, leading to many-body localization, prevents runaway heating and enables the observation of coherent quantum dynamics at high energy densities. Furthermore, we clarify the distinction between the equilibrium and Floquet SPT phases by identifying a unique micromotion-based entanglement spectrum signature of the latter. Finally, we propose a unifying implementation in a one-dimensional chain of Rydbergdressed atoms and show that protected edge modes are observable on realistic experimental time scales.The discovery of topological insulators-materials which are insulating in their interior but can conduct on their surface-has led to a multitude of advances at the interface of condensed matter physics and materials engineering [1][2][3][4][5]. At their core, such insulators are characterized by the existence of nontrivial topology in their underlying single-particle electronic band structure [6, 7]. Generalizing our understanding of topological phases to the presence of strong many-body interactions represents one of the central questions in modern physics. Some of the simplest generalizations that have emerged along this direction are symmetry-protected topological (SPT) phases [8][9][10], which represent the minimal extension of topological band insulators to include many-body correlations. Featuring short-range entanglement, SPT phases do not exhibit anyonic excitations in their bulk, but nevertheless possess protected edge modes on their surface; as a result, they represent a particularly fertile ground for studying the interplay between symmetry, topology, and interactions.While indirect signatures of certain ground state SPTs have been observed in the solid state [11][12][13], directly probing the quantum coherence of their underlying edge modes represents an outstanding experimental challenge. In principle, cold-atom quantum simulations could offer a powerful additional tool set-including locally-resolved measurements and interferometric protocols-for probing the robustness of edge modes and systematically exploring their stability to specific perturbations [14][15][16][17][18]. Moreover, such platforms could also enable the controlled storage and transmission of quantum information [19][20][21]. Despite these advantages, and owing to the complexity of typical model SPT Hamiltonians, it remains difficult to engineer and stabilize SPT phases in coldatom systems. One approach to t...