GMAT Sentence Correction (SC) | By the late 1960s, the rising number

Hi all,
Can anyone please elaborate more in the usage of "by the time" at the beginning of the sentence?
I am familiar with only such a form of "by the time x,y";y happen after x.However,there is no x in this context.
What is the time frame of this context?

Moreover,is the preposition "to" or "for" a split in this question?

Thanks