简单的英语句子结构分析问题

倒装句。
only引导时间状语从句when humanity began to get its food in a more productive way.
因为这部分状语前置，所以主谓要倒装。
还原过来就是
there was time for other things only when humanity began to get its food in a more productive way.

这个句子其实是 there be 句型 结合了一个倒装句。
Only when放句首，后面的句子要倒装，
这个句子本来是There was time for other things only when humanity began to get its food in a more productive way .
只有当人们用更有效率的方法获取食物时，才有了做其他事情的时间。