Oh, it does happen. One of the earliest examples is King Ashoka. He lived just a couple of centuries after the Buddha, and he was involved in quite bloody military campaigns, until he converted to Buddhism. After that, he went on tours preaching the dharma, he encouraged dharma teachers, he put up pillars with dharmic texts on them and he ended up emperor of much of India. In that way he helped the dharma to spread over much of India.

Here is a photo of one of his pillars.

Ashoka Pillar, Allahabad, 1870

Buddha himself wandered around Northern India as a monk, with his begging bowl, and he taught anyone who wanted to learn from him. He first taught his five companions who had been following the path of asceticism with him, before his sudden change of direction towards the “middle way” when he became enlightened. So those were the first five people to follow his path.

He ended up having thousands of followers, who were drawn towards the teachings. Some just heard the teachings through hearsay from someone who had heard Buddha teach, and repeated his words to them, and immediately “got it” the essential meaning of what he was teaching. They must have been very receptive to the teachings to do that.

So - it’s often like that - spreading of the ideas. People hear of them. Nowadays you may read books, watch videos. In my case it was through a friend who I met who became a Buddhist nun shortly after I met her, and we talked a lot about the Buddhist teachings and I decided I wanted to follow that path myself eventually - after a fair while of listening to many teachings.

So there are many ways that the Buddhist teachings spread. Nobody says “go out and convert everyone to Buddhism” as happens in the more evangelical Christian churches.

But there’s no reason why one shouldn’t try to spread the teachings, and debate them with others etc, if one is in a position to do so and you feel that it is helpful to do so. Or in other ways, publishing books, building retreat centers, supporting teachers. It’s just a matter of ones own individual decisions.

It’s a bit like, say, astronomy. If you are keen on astronomy, you will tell people about it, anyone who is interested to listen. You might write a book on it. You might run a planetarium, or show the night sky through your telescope. That’s all proselytizing in a way. But you don’t feel “I have to convert everyone to astronomy” :). Yet, if you think it is worthwhile, interesting, inspiring, you naturally want to share this with others. So, proselytizing in this general sense is a natural thing, and of course, Buddhists proselytize about their faith too.