We do know that for the lucky ones on which SSRIs do work, it seems to reverse some of the brain structure changes associated with depression -- some abnormally small parts tend to grow thicker. The reversal can be seen at one week after the start of medication use, before one can even tell whether an antidepressant has started working (a commonly-cited duration would be 2 weeks).
[1]: https://www.nature.com/articles/s44220-023-00187-w