I wouldn’t describe Buddhism as an “alternative” to atheism. Atheism and Buddhism are quite compatible. The concept of a personal god just doesn’t enter into Buddhism, so non-belief isn’t an obstacle to Buddhist practice.
Buddhism doesn’t rely on a body of beliefs. The only “belief” that’s essential to Buddhist practice is that it is possible to directly experience the nature of reality. If you don’t believe this, then there really is no point in practicing Buddhism. If you can accept this possibility, then Buddhism offers a set of practices that open the door to that experience.
In fact, in the end, it’s necessary to drop all beliefs of any kind in order for that door to be opened. This includes beliefs held by many secularists. A strictly materialist view would be as much of an obstacle as would belief in a personal God. What’s required is complete openness, without attachment to any idea about the way things are. Secularists are not immune to attachment to ideas.
A staunch secularist would likely be put off by many of the more devotional aspects of traditional Buddhist practice. There’s a lot of ritual, a lot of liturgy, things that have no good rational explanation. Buddhism values questioning greatly, but “what”, “when”, “who” and “where” are far more important than “why”. “Why” tends to be the darling of secularists.