To answer this question, one has to choose how to quantify "the warping of space-time". In general, it takes 20 numbers (independent components of the Riemann curvature tensor) at every point to specify how spacetime is warped!
A reasonable approach is to look at the Ricci scalar curvature $R$, which boils down this complexity into a single number. In a homogeneous and isotropic spacetime such as ours, it is just a function of cosmological time, $R(t)$, because it is the same at all points in space. Using the usual spatially-flat Friedmann metric for describing our universe, it is given by
where $a(t)$ is the Friedmann scale factor. So if we know how the scale factor evolves with time, we know how the scalar curvature evolves with time.
The evolution of the scale factor is complicated because in different eras different types of energy dominate in the universe. Let's simplify by looking at three cases where only one type of energy dominates.
If the universe is filled with only matter, then
Plugging this into the equation above gives
so the curvature steadily decreases.
If the universe is filled with only radiation, then
so the curvature vanishes!
If the universe is filled with an inflaton field or dark energy, then
which is a constant.
In none of these cases does the curvature ever increase with time.
So, without doing a more detailed analysis combining matter, radiation, and inflation or dark energy, we find that the warping is maximum at the Big Bang (it was infinite, according to classical General Relativity, when the universe was a point) and has been decreasing ever since as the universe has expanded.