人間は持たざる時には人並みを求めるが、一度人並みになるや、今度は人との違いを求めだし、人と同じ商品では満足できなくなるからだ
At first I thought し indicated reason, but からだ already indicates reason, so し here would be redundant.
The し
is just part of a normal conjugation of the verb 求め出す
-> 求め出し
. It would be clearer if it were written with the kanji for 出す
, but when combined with other verbs it's sometimes just written だす
like it is here.
You can read more about verb+出す
here and here, and a little about the criteria for using kanji or not in cases like this here.