Short answer: The best time to use beard oil is right after a warm shower, because this will open up the pores under the beard and allow the oil to be absorbed more easily to reach the hair follicles for maximum benefit.
The cool thing about beard oil is that there is absolutely no wrong time to use it. But the best time to use it is right after a shower. This is because the warm water actually opens up all the pores on your skin under the beard. This makes it easier for the oil to penetrate the skin and become absorbed much more easily. So once it is absorbed an soaked into the skin lying under the beard, this will maximize the benefits of the oil, since it has penetrated the hair follicles and will actively nourish, hydrate and condition the beard for a rich, soft feel. Not only that. The deeper the oil goes into the follicles, the more stimulation for growth. So this is why you often hear many bearded brothers say that the best time to apply the oil is right after a nice, long shower.
Generally, it is preferred to use beard oil at least once a day, and the best time to do that is after a morning shower. If you dont shower in the morning, then you can just apply it after washing your face. It would be even better if you apply it twice a day, and as mentioned, you can simply wash your face with warm water for a minute or so right before applying the oil.