As you've discovered, the ordinary order of English declarative sentences is subject first, verb following, but there are a number of rhetorical or informatic reasons to invert that order. One is that speakers tend to put old information before new information, and another is that speakers prefer to place weightier (i.e., more grammatically-complicated) structures at the end of a sentence. It's likely both principles are operating here.
In your sentence
A (adjunct) = Along with the rise of agricultural societies
B (subject) = the development of property ownership and the need to keep records of it
The ordinary order would have
B came A
But my guess is that the paragraphs preceding the sentence had already introduced the topic of the rise of agricultural societies. So that's old information. And the sentence is introducing the new idea of property ownership and record-keeping.
Now, note that A is two prepositional phrases, one using along with; the other, of. Light and simple.
Contrast that with B, which has the structure of a compound noun phrase -- the development ... and the need .... The first noun phrase has a modifying prepositional phrase (of property ownership), and the second noun phrase has an infinitive complement (to keep records), which itself has a modifying prepositional phrase (of it), with a pronoun (it) having an antecedent (ownership) in the first noun phrase. Heavy and complex.
So the principles of old-before-new and light-before-heavy work to invert the ordinary sequence to
A came B.
It is easy to conjure examples of the operation of these principles:
Because of his aforementioned pro-Nazi sympathies, a virtual exile to the Bahamas
for the duration of the war was the Duke of Windsor, formerly King
Edward VIII, a man who had abdicated the British throne to marry an American divorcee.
Without the "aforementioned" signaling an old piece of information and without the "heavy" addition of the appositive, the subject (exile) and the nominative complement (the Duke of Windsor) would more naturally be reversed:
The Duke of Windsor was a virtual exile to the Bahamas for the duration of the war because of his pro-Nazi sympathies.