In that context, "since" and "ago" could both be prepositions (both also go to make up various prepositional phrases, and also have varying uses as conjunction, adverb or adjective in some cases).
Unfortunately, English has fairly stringent and arbitrary rules of usage concerning propositions and the way they combine with other parts of speech. The combination "ago since" isn't allowed as you used it.
Just something you have to know I guess - a bit like how to spell your own name.
So, long story short: it's idiomatic.