I read before that General Relativity can be derived from symmetries, but what I don't know is whether this means that symmetries alone can derive General Relativity or if this means that symmetries combined with additional information can be used to derive General Relativity.
For comparison if one said that special relativity can be derived from symmetries that could be interpreted to mean that special relativity can be derived from those symmetries combined with the speed constant. If however we knew nothing about a speed constant, length contraction, time dilation, or electromagnetism, and the only information we had related to special relativity, then we wouldn't have enough information to derive special relativity, as Euclidean Space, and Galilean Spacetime have all the symmetries that Spacetime in Special Relativity has.
Let's say that we didn't know about the existence of black holes, gravitational lensing, or gravitational interactions. The only information we had related to General Relativity were the symmetries of General Relativity, that there is a speed constant, and that spacetime is curved near a massive body. Would we have enough information to derive General Relativity in this case?
To be clear when I say the speed constant I'm referring to the speed that massless particle move at.