Methodism is usually described by its discipline, the small group meetings, the methodical rounds of prayer and self-examination that gave the movement its mocking nickname before its followers embraced it. Hymns and Sacred Poems shows the other half of how the movement actually worked on a person. Rather than argue a doctrine from a pulpit and hope a listener absorbed it, the Wesleys put the doctrine directly into the first person and handed it to the congregation to sing themselves. And Can It Be does not describe someone else's astonishment at grace, it performs the singer's own, marveling that God himself should die for the one singing the words. A worshiper singing it is not being told what assurance of salvation feels like, they are rehearsing the sensation of having it, verse by verse, in their own voice, alongside everyone else in the room doing the same thing.
That was the specific theological argument early Methodism was making against much of the Protestantism around it, that a believer could know their own salvation with confidence rather than spend a lifetime hoping for it without certainty. A sermon can assert that claim. A hymn a congregation sings together, using the first person the whole time, puts the congregation in the position of asserting it about themselves, together, every time they sing. That mechanism, doctrine delivered as personal testimony set to a singable tune, is what later generations meant when they said Methodism was born in song as much as in preaching, and Hymns and Sacred Poems, however patched together from other people's material, is where that particular voice first reached print.