… excavations revealed a sequence of early structures preceding the major rebuilding by Asoka

See this post by Bhante Sujato explaining that it’s quite expected that Maya would haven given birth at a pre-existing shrine. And see this response by Richard Gombrich further refuting the paper’s proposed chronology.

Still, the paper does inform us a bit about the site as Maya must have found it: a ~200-year-old outdoor shrine with thick wooden fencing around a central tree.