Stable marriage of a two-sided market with unit demand is a classic problem that arises in many real-world scenarios. In addition, a unique stable marriage in this market simplifies a host of downstream desiderata. In this paper, we explore a new set of sufficient conditions for unique stable matching (USM) under this setup. Unlike other approaches that also address this question using the structure of preference profiles, we use an algorithmic viewpoint and investigate if this question can be answered using the lens of the deferred acceptance (DA) algorithm without actually running the algorithm. Our results yield a set of sufficient conditions for USM (viz., MP and MR) and show that these are disjoint from the previously known sufficiency conditions like sequential preference and no crossing. We provide a characterization of MP that makes it efficiently verifiable (without using DA), and shows the gap between MP and the entire USM class.