Scott,
I don't think you quite mean that, otherwise you have to place the starting of the church considerably later than most Reformed people do. It's certainly not the conventional EP view.
The psalms (as such) begin with the time of David in preparation for the temple, even though an earlier song by Moses (Psalm 90) was incorporated into the psalter. By the way, the psalter as a collection is clearly post-exilic, since it includes psalms that make reference to the exile in Babylon (e.g. Ps 137). There were earlier collections of psalms, it appears (see the end of psalm 72), but it's not clear at what point we can speak of a "psalter" as the hymnbook of the temple in the sense in which EP often does. Certainly, with respect to the first temple, it was not our present psalter. (There are also additional psalms floating around in the Septuagint and at Qumran which some clearly regarded as canonical, which complicates the issue further).
There was no singing in the tabernacle liturgy, as far as we can tell, though there were worship songs beign sung informally in a number of contexts (exod 15; Judges 5 etc). Most modern scholarship also argues that there was no singing in the synagogue either, prior to 70AD, when a number of temple features carried over into the synagogue. My own view is that singing in the early church was an innovation, reflecting the church as new temple, which may subsequently have influenced the synagogues. We just don't have the data to be sure, however.
All this to say that the question of what the church sang and when (and where and why) is a lot more complex than most people (on both sides of the question) realize. I deal with it in a chapter of my Biblical Theology of worship, which unfortunately is still a long way from publication (since it requires me to research an enormously wide field of study).