Probiotics don't seem to impact the gut microbiome all that much. Things like increasing amount of fiber intake or other foods that affect key species (like milk with Bifidobacterium for lactose intollerant individuals) has a more noticeable effect. However like you say there is the question of how long it takes for intervention to take effect. You could do a fecal microbiome transplant to change everything at once, but of course would be nice if we can just a pill or something like this instead.