You need a hypothesis about the time or frequency characteristics of the signal. If the signal is strictly periodic, then you can try to find the shape of the signal by the method of overlapping epochs. Try to find the right period.

If the signal is non-periodic, then its reconstruction is impossible.

The reconstruction of a sub-sampled signal by ideal low-pass filtering is affected by aliasing error. We have written the attached article about the aliasing error and some bounds of this error.