But if you're trying to explain why Django is spelled the way it is, it's far more insightful to explain /d/ -> <d> and /ʒ/ -> <j> than to posit the <d> comes from nowhere and is just silent.
"the English "j" and the French "dj" represent the same sound"
Secondly, I wanted to dive in a bit more and explain the relationship between the "j" in English vs French and hence the role of the "d" in the French spelling (as that's kind of the whole point).
Phoneticists commonly represent the English "j" sound as the amalgam of two separate sounds:
(a) English "d", a common enough sound; and
(b) the somewhat less common "zh" sound, the second consonant sound in "beige".
In French†, these two sounds are separately written as "d" and "j", and combined (try it—speak quickly) they make the English "j" sound.
This is what everyone has been trying to explain with the unfortunately obscure IPA references.
† – Likewise in other languages, per my examples above. For example, in Russian, the two sounds are separately denoted "д" and "ж" and combine to form the English "j" sound, as in "Джугашвили" (which is Georgian, really: "ჯუღაშვილი").
Basically: 1. "d" in French is pronounced "d". 2. "j" in French is pronounced "zh". 3. "dj" in French is pronounced as the same affricate you get by combining "d" and "zh". 4. This is a better explanation for the "dj" in Django rather than saying the "j" is an affricate and the "d" is silent.