It's hard to get a congregation of people who are not great at singing into the frame of mind to sing. Sometimes a little meditation or introduction can help, to signal the change of gears and to establish the song leader as someone to trust and follow during the singing. It is important that this doesn't degenerate into rambly, meaningless waffle.
Another option that I just thought of today was a long musical introduction to the first song. This gives time to shift into a more musical, emotional frame of mind.