Chronology of Slavonic palatalisation?

The textbooks of Old Church Slavonic I have explain the relationship
of the three separate palatalisations of the velars to each other. For
example, the change of k, g, and x into c^, z^, and s^ when followed
by a front vowel or soft liquid sonant happened before the other
two. However, can these three developments be located chronologically?
The first palatalisation seems to have occured after the Slavs came
into contact with the Germans, so can that fact help to track down the
century in which it took place?

I believe I have read somewhere that all palatalisations occured in
the first millennium A.D., but the five or six hundred years between the
birth of Christ and the breaking up of Common Slavonic seems like a
too brief time for so many changes.

Christopher Culver