Various factors affect rennet coagulation and consequently cheese yield, but the subject of research has been mainly the cow milk. For the purpose of goat cheese production optimization, this paper investigated the influence of enzyme concentration (0.01–0.054 g/L), pH (6.5–6.1) and temperature (27–35 °C) on rennet coagulation of goat milk. Coagulation time (RCT), aggregation rate (AR), and gel firmness (G’60 and GF), were measured by oscillatory rheometry. The decrease in rennet concentration extended RCT. At lower rennet concentrations, a lower AR was recorded, which ranged from 0.02 Pa/s to 0.05 Pa/s. The decrease in pH from 6.5 to 6.1 caused a two times shorter RCT, and a two times faster AR. There was no effect of pH on the firmness of the rennet gel. The increase in coagulation temperature from 27 °C to 35 °C reduced the RCT of pasteurized milk from 12.6 min to 8.6 min, and caused a linear increase in the AR, but did not significantly affect the firmness of the gel. The present study revealed that the optimization of the rennet coagulation process could be directed towards pH lowering, or temperature increase, since they accelerate the process, but do not alter the examined gel firmness parameters.