Estimate input from measuring only RC filtered input
That's certainly possible, assuming you know the values of the resistance and capacitance $R$ and $C$. You can expand the signal $V(t)$ in a Taylor series about $t=0$ to arrive at an approximate linear model. First, remember the Taylor series of the exponential function:

$$
e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = 1 + x + \frac{x^2}{2} + \ldots
$$

If you're assuming a linear model near the step input time of $t=0$, then truncate the sum to arrive at:

$$
e^x \approx 1 + x
$$

Substitute this into the equation for $V(t)$ to yield:

$$
V(t) \approx V_0\left(1 - \left(1 - \frac{t}{RC}\right)\right)
$$

$$
V(t) \approx V_0\frac{t}{RC}
$$

Which is a pretty simple result. If you know the absolute time of the step input, then you theoretically don't even need multiple measurements; you could estimate $V_0$ directly using:

$$
V_0 \approx \frac{V(T)RC}{T}
$$

where $T$ is the time at which you measure the signal. If you don't know the exact time at which the step is input, then you can take two measurements, as you suggested, at times $T_1$ and $T_2$, then form the estimate as follows:

$$
V(T_2) - V(T_1) \approx V_0\frac{T_2}{RC} - V_0\frac{T_1}{RC}
$$

$$
V_0 \approx RC \frac{V(T_2) - V(T_1)}{T_2 - T_1}
$$