I have heard many people compare it to a graduation, but a graduation is really just a ceremony to show a level of proficiency; an arangetram is an actual concert. I want to be able to share the significance of the event with a Western audience who know nothing about Carnatic Music nor its traditions.

I'd probably be more of a help if I knew what an "arangetram" was exactly. Try explaining it to 'em with a step-by-step.

you should use a accent which will help and give nick names to your steps so they find it easier to understand in your own way.

for example there are steps like screwing a lightbulb and feeding a dog for the most common dances

maybe you could say its like a recital,combined with Indian musical traditions,which makes it more of a performance than a graduation.

"debut" is the word.
debutante:a young woman making her debut into society

Let us be clear in our minds. It is the beginning of entering a (serious)musical 'career' to be shaped as a musician. It is not a graduation, it is demonstration of talent/proficiency toward performing. Certainly not the end state of attaining that which is what most atleast in the United States make it sound.