I was reading the 1960 edition of well-known Unitarian minister and liturgist Von Ogden Vogt's Art and Religion that explained his vision of the opening part of worship. This is his chapter "The Order of Liturgy" -- so influential that it's cited as a such here. The following chapter "Introit and Antiphons" anticipated a revival of that liturgical use among mainline Protestants, but which have little purchase among Unitarian Universalists.
The book's in copyright, but the original 1921 edition is in the public domain: that's what follows. And if there's any difference between 1921 and 1960 in these two chapters (there is an appendix) it has escaped my attention.
Von Ogden Vogt is important for understanding the influential -- if now little used -- Services of Religion that prepend the joint Unitarian and Universalist red Hymns of the Spirit. There's no doubt in my mind that he's behind making an introit an option for the services, though, as he explains in Art and Religion, these ought to be composed afresh. What he doesn't write about is the sequence, particular to Unitarians so far as I've seen, of
- Opening words
- Confession (sometimes broadly conceived)
The exhortation (which also sets the tone of worship) is the innovative part, and fills the role of the introit.