It is true that the shofar is blown during the days of Elul to warn the people that Rosh HaShannah is approaching (when the Day of the LORD will begin) and that this is the season for Teshuvah (repentance).  However, from what we have learned, the trumpet blown at the beginning of Elul is not called "the first trump".
 
According to Joseph Good of Hatikva Ministries in Texas there are three named shofars:
the "first shofar" (first trump), the "last shofar" (last trump) and the "great shofar".
 
  The "first shofar" (first trump) is blown at Shavuot - Feast of Weeks, also known as Pentecost. This is the BETROTHAL.  This shofar was blown in Exodus 19 when Torah was given. Also at this same festival the Holy Spirit came upon the believers.
 
The "last shofar" (last trump) is blown at Yom Teruah  - meaning "day of the awakening blast" also known as Feast of Trumpets and Rosh HaShannah.  This is the WEDDING and also the coronation of the King.
 
The "great shofar" is blown at Yom Kippur.
 
Joseph Good teaches these things in his book "Rosh HaShanah and the Messianic Kingdom to Come"  I appreciated very much your post.  There is so much to learn from the Jewish roots of our faith.
 
Shalom,   Roberta.