Single-crystal transition metal dichalcogenides (TMDs) and TMD-based hetero-junctions have recently attracted significant research and industrial interest owing to their intriguing optical and electrical properties. However, the lack of a simple, low-cost, environmentally friendly, synthetic method and a poor understanding of the growth mechanism post a huge challenge to implementing TMDs in practical applications. In this work, we developed a novel approach for direct formation of high-quality, monolayer and few-layer MoS2 single crystal domains via a single-step rapid thermal processing of a sandwiched reactor with sulfur and molybdenum (Mo) film in a confined reaction space. An all-solid-phase growth mechanism was proposed and experimentally/theoretically evidenced by analyzing the surface potential and morphology mapping. Compared with the conventional chemical vapor deposition approaches, our method involves no complicated gas-phase reactant transfer or reactions, and requires very small amount of solid precursors [e.g., Mo (~3 μg)], no carrier gas, no pretreatment of the precursor, no complex equipment design, thereby facilitating a simple, low-cost, and environmentally friendly growth. Moreover, we examined the symmetry, defects, and stacking phase in as-grown MoS2 samples using simultaneous second-harmonic-/sum-frequency-generation (SHG/SFG) imaging. For the first time, we observed that the SFG (peak intensity/position) polarization can be used as a sensitive probe to identify the orientation of TMDs' crystallographic axes. Furthermore, we fabricated ferroelectric programmable Schottky junction devices via local domain patterning using the as-grown, single-crystal monolayer MoS2, revealing their great potential in logic and optoelectronic applications. Our strategy thus provides a simple, low-cost, and scalable path toward a wide variety of TMD single crystal growth and novel functional device design.