How can I estimate Roll from Position?
You can, but the accuracy is going to be somewhat poor.

Given the positions you can approximate the path with your favourite line approximation method. The important thing is that it can give you continuous evaluations (no jumps and no discontinuities) of at least the first and second derivative. Third order algebraic splines are a good approach.

Note that you will need to map Latitude and Longitude to some Cartesian representation. Depending on the length of the flight, a "flat earth" approximation might or might not be a good idea.

With these, assuming that each manoeuvre was mostly flat(*), you can compute your local curvature:

$$k = \frac{x'y'' - y'x''}{\sqrt{(x'^2 + y'^2)^3}}$$

Now you can estimate your bank angle $\phi$ with

$$\phi = atan\left( \frac{k \cdot V_{tas}^2}{g} \right)$$

where $g$ is Earth's gravity.



(*) the formula is for a manoeuvre in the x-y plane. You could turn your coordinates so to have a local x-y plane that is coincident with the plane where the aircraft was manoeuvering, but then you could not use the bank angle formula, that is correct only for turns in the horizontal plane (thanks Jan Hudec for correcting)