Buddhism has definitely engaged in missionary work. The Buddha himself gave a Great Commission of his own, similar to the one Jesus gave...
"Go forth, O bhikkhus, for the good of the many, for the welfare of the many, out of compassion for the world. Let no two of you go in the same direction, teach the Dhamma that is beautiful in the beginning, middle and end, expound both the spirit and the letter of the holy life completely fulfilled, perfectly pure. There are beings with but little dust in their eyes, who not hearing the Dhamma will decline but who, if they do hear it will grow"
After the Buddha, there was also King Ashoka who sent missionaries throughout S/SE/SW Asia, and also Buddhist monks going into China via the Silk Road.
Buddhist missionaries / monks have historically used different techniques than say, Christian missionaries, but it is absolutely a universalizing faith with a commission to spread.
Edit to add: historically speaking, Buddhism is the oldest universalizing religion.