Inconel 718 is a widely used superalloy, due to its unique corrosion resistance and mechanical strength properties at very high temperatures. Hot metal extrusion is the most widely used forming technique, if the manufacturing of slender components is required. As the current scientific literature does not comprehensively cover the fundamental aspects related to the process–structure relationships, in the present work, a combined numerical and experimental approach is employed. A finite element (FE) model was established to answer three key questions: (1) predicting the required extrusion force at different extrusion speeds; (2) evaluating the influence of the main processing parameters on the formation of surface cracks using the normalized Cockcroft Latham’s (nCL) damage criterion; and (3) quantitatively assessing the amount of recrystallized microstructure through Avrami’s equation. For the sake of modeling validation, several experimental investigations were carried out under different processing conditions. Particularly, it was found that the higher the initial temperature of the billet, the lower the extrusion force, although a trade-off must be sought to avoid the formation of surface cracks occurring at excessive temperatures, while limiting the required extrusion payload. The extrusion speed also plays a relevant role. Similarly to the role of the temperature, an optimal extrusion speed value must be identified to minimize the possibility of surface crack formation (high speeds) and to minimize the melting of intergranular niobium carbides (low speeds).