The quick answer is that the average american probably did not have much perception of Buddhism other than it was some sort of enigmatic asian religion that involved monks and statues of its founder and perhaps a general sense that Zen Buddhism entailed a relaxed "go with the flow" mentality. That said, for a subset of the culture, there was intense interest in and engagement with Buddhism. Especially Zen Buddhism.

The first western engagements with Buddhism that went beyond university academic scholarship were wealthy spiritual seekers in Europe and the Eastern United States. You find early echos of this type of interest in the writings of Transcendentalist philosophers who were influenced by eastern spirituality in general. An example of this interest is that the first western translation of the Lotus Sutra (an important Buddhist scripture) was published in a Transcendentalist publication called "The Dial".

The next major phase of Western engagement with Buddhism were individuals who were interested in Buddhism as an actual practice. This often took the form of syncretistic movements such as Theosophy. This interest ranged from individuals being influenced by Buddhism to outright conversion.

A notable element of this interest and engagement with Buddhism was that Buddhist philosophy and psychology was often viewed outside of its cultural context of ritual and practice and seen as a purely rational and even scientific view of life and reality. When the cultural, ritual and "religious" aspects of Buddhism were addressed they were often seen as naive perversions of the "pure" teachings of the Buddha himself. This is a general western approach to Buddhism engagement that has persisted to this day.

A driving force in this view of Buddhism was the scholarship and writings of DT Suzuki and later Alan Watts. Suzuki presented Zen to western audiences as a form of "pure religion" that entailed direct intuitive comprehension of reality and transcended discriminating consciousness and societal norms. While there is some small truth to this view, it presented an overly narrow view of Buddhism that often lacked cultural and practice context.

This is the view of Buddhism in general and Zen in particular that was embraced by the "Beat Generation" and later the "Hippy Movement". These members of society viewed the culture they had grown up in as overly materialistic, conservative, violent and lacking true spirituality. Eastern spirituality in general and Zen in particular was highly attractive to them because it seemed to embody all of the opposite traits of what they saw as problems in their culture. A peaceful approach to living that involved transcending cultural norms and having direct experiences of spiritual enlightenment was highly attractive to them. This dynamic was certainly accelerated by the generational experimentation with psychedelic drugs. Many people had mystical and spiritual experiences while taking these substances that seemed tantalizingly similar to what was found in eastern spiritual texts.

If you would like to drill into any of this, please let me know and I can share some citations for further research.