The only thing wrong with your translation is the rendering of “taking orders”; it’s “recevoir des ordres”. However, that’s not the only possibility; in particular you can keep the word “since”.

• Trois jours seulement avaient passé depuis que j’avais commencé à recevoir des ordres.

CORRECTION

There has been an oversight from my part; it has been caught by mcadorel (see the comments); the OP’s translation is also a possibility.

Your sentence is correct outside prendre les commandes which more often means “taking control” in French.

What you want to say can be written unambiguously:

Ça ne faisait que trois jours que j’avais commencé à prendre/accepter des commandes.

Ça fait becomes, with changing the tense, ça faisait, ça fera, ça ferait, ça aurait fait…

Yes, “ça fait” can become “ça faisait” if you want to speak about the past.

The part “que j’avais commencé à prendre les commandes” sounds a little bit weird.
Maybe use “ça ne faisait que trois jours que j’avais pris les commandes” because in french we understand that you started 3 days ago.

I just want to add one thing : “ça fait” and family (“ça fera“, “ça faisait“..) are speaking language. Do not write it down. Instead you should use the ‘full’ word for “ça” wich is “cela“.
Like this sentence : “ça fait trois jours que je marche” becomes “cela fait trois jours que je marche“.
However it doesn’t work everytime if you want to use “cela” instead of “ça“. For instance, “ça va?” (How are you?) can’t be “cela va?” because if you uppgrade the “ça” to “cela” you also have to upgrade the “va” to “va-t-il” and add a “Comment“. So “ça va?” becomes “Comment cela va-t-il?“