The Ising-like model is used to simulate the thermal behavior of a 2D spin crossover (SC) nanoparticle embedded in a matrix, which affects the ligand field at its surface. First, we discuss the standard case of the isolated nanoparticle, and in the second part we consider the effect of the interaction between edge molecules and their local environment. We found that in the case of an isolated SC nanoparticle presenting a gradual spin transition, the matrix effect may drive a first-order spin transition accompanied with a hysteresis loop. An in-depth analysis of the physical mechanism underlying this unusual property is performed, leading to build up the system's phase diagram which clarifies the conditions of appearance of the first-order transition in the current 2D SC nanoparticles as function of their size and the strength of their interaction with their immediate environment.