Here is a particularly good set of articles (and some wonderful artwork)
about Rosh Hashanah.

It is from the templeinstitute.

http://www.templeinstitute.org/rosh_hashana/introduction.htm

It again seems to indicate that Rosh Hashanah would not start until two
witnesses who had seen the first sliver of the new moon would arrive at the
Temple in Jerusalem and give witness, under cross examination, of what they
had seen.  Then, the sacrifies and trumpet blasts (including the shofar)
would be sounded.

In Christ,
Erik