I will try and be as concise and clear as possible, but I'm still trying to understand my own question.
Timelike observers can move freely through space, which allows them to set up experiments such as a red shift/blue shift experiment in a Schwarzschild spacetime. If the observers are at different radii stationary from the event horizon, they will experience different relative rates of time given by $$d\tau^2 = -\left(1- \frac{2M}{r}\right)dt^2 + \left(1- \frac{2M}{r}\right)^{-1}dr^2 + r^2 d\Omega^2$$ This is because $g_{00}$ is a function of $r$.
It is not possible, however, for two observers to remain stationary at two different points in time. It is also not possible for a single observer to send a signal from one point in time and receive that signal at the same point in space but a different point in time. This is baked into the causal structure of spacetime, it is unavoidable.
So in the FRW metric, for example, we can set $g_{00} = 1$ because it is possible to normalize away any $g_{00} = f(t)$ such that $g_{00} = 1$. Also known as a lapse function.
I turned to the Landau-Lifschitz pseudotensor for some possible insight into the gravitational potential across time and computed the $t^{00}$ value for the FRW spacetime as $$-6 \frac{\dot{a}^2}{a^2}$$
I'm not sure what to make of this.
To summarize: even when spatial separation does not exist, is there still a gravitational potential? (only across temporal separation, such as past to future)