Even before we accept our first jobs, or begin our careers,

The reason of having a comma is to explain that "begin our career" is a parallel or further thought of the original statement "accept out first jobs."

The two phrases present essentially the same idea. Our first job is a bit plainer, and the author chooses to use a fancier word, career, to augment the original thought.

Here is another example:

Would you like a cup of coffee, or cappucino?

And, compare it with:

Would you like a cup of coffee or tea?

In the coffee/cappucino case, you don't really have two choices, since cappucino is a kind of coffee. The speaker "adds on" the cappucino part to the question, and in that situation, you need to add a comma.

In the coffee/tea case, you indeed have two distinct choices, and so there is no comma.

If you write as:
Even before we accept our first jobs or begin our careers we all learned how to negotiate.

You'll find it's too long for one sentence, with several verbs, nouns & proper nouns. But if we put a comma at a proper position(s), we'll find the sentences are smoother, clearer & more convincing.

Even before we accept our first jobs, or begin our careers, we all learned how to negotiate.