From the perspective of one experiencing time-dilation nothing appears unusual, everything appears normal, it only from the outside perspective that things are strange.
As far as I can tell the singularity happened in the late 1700's. For thousands of years the collective economic growth of the world was effectively a straight shallow line, it grew, but slowly and linearly, then in the late 1700's something changed, it went exponential and everybody was along for the ride, and from the perspective of being caught up in this exponential growth it appears flat, normal even. but you look at history and wonder why every advance was so slow. and you look ahead and say the singularity is almost there. But we will never actually reach it. by the time we get there it is the new normal.