Devanagari -A script without a language?

The Indic branch of IE Family of languages
consists of more than a dozen living languages. It is believed that
all these languages use a script called "Devanagari' script .This
script is a fully developed script with vowels and consonants
structured in a perfect manner.
Linguists are aware that in a natural language
speech develops first, followed by development of script ,perhaps,
after sufficient period of folk-songs,cultural and intellectual
development.Many spoken languages do not have a script at all.
While `script' is not a must for a language, a sufficient phase
of `spoken language' is a condition precedent for formation of script
based on phonology. This is so because the `script letters' represent
the sounds of the spoken words, in phonetic languages.(However in non-
phonetic languages, the chances of `pictographic script' developing
prior to `speech' cannot be ruled out.)
Indian History or World History does not have
any evidence to prove that there was a language called `Devanagari'
and it was spoken by any people, for a significantly long
period.Then, the question that baffles is `How did this script
develop?'Can any IE scholar throw some light on this riddle?

A.S.Sundar,