This site's own FAQ addresses this directly: there is no responsible universal timeline for any supplement in this category. Gut-microbiome changes are generally gradual.
Rather than manufacturing a specific week-by-week promise, this site states plainly that some sources suggest early digestive changes within the first couple of weeks, with fuller effects building over 1 to 2 months — worth crediting that honesty over an invented instant-results timeline.
Since fuller effects are described as building over 1 to 2 months, the 3- or 6-bottle package gives more room for a fair trial than the smallest 2-bottle option, per this site's own gradual-timeline framing.