This is a good example of how causality is not always straightforward.

Serotonin reuptake inhibitors do work and work better the better in people with more severe depression symptoms.

However they generally can only be expected to work after around 2-4 weeks where as the serotonin increase is on day 1.

The mechanism isn't exactly "more serotonin = more happy" but that's a bit complex for most people.