Have you tried to make the delay seconds a zero? Here is the documentation description to the Delayed announcements in a hunt group.
First Announcement Delay (sec)
Enter the number of seconds that a call remains in queue before the associated
first announcement is given the calling party. The call retains its place in the
queue while the caller is listening to the recorded announcement. If the call hasn
’t
been answered after the announcement, the caller hears music (for first
announcement only) if Music-on-Hold is provided or ringing for as long as the
call remains in queue. Appears only if the Queue field is
y and the Vector field is
n
.
Valid entries Usage
0
through 99 When 0 is entered, the first announcement is provided
immediately to the caller. This value is set automatically to
0
if there is no queue.
blank This field must be blank if there is no first announcement.