Can one derive Einstein's field equations form the first law of horizon mechanics? Many papers explored how the first law of horizon mechanics ("energy conservation") can be derived from general relativity's field equations. This started in the 1970s.
Is there any literature on the opposite way: Can one derive the field equations from the first law?
Maybe some additional assumptions are needed, but it should be possible.
Edit: Is there any literature beyond Jacobson and Padmanabhan?
 A: In addition to Jacobson's paper suggested in comments I would recommend looking at works of Padmanabhan, for example the essay:

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*Padmanabhan, T. (2008). Gravity: the inside story. International Journal of Modern Physics D, 17(13n14), 2585-2591, doi:10.1142/S0218271808014114, free pdf.

Which outlines the following sequence of steps for deriving EFE's (or rather field equations of Lanczos-Lovelock gravity for which EFE's are a specific case) from the laws of horizon  mechanics:
Principle of equivalence
$⇒$ Gravity is described by the metric $g_{ab}$
$⇒$ Existence of local Rindler frames (LRFs) with a horizon around any
event
$⇒$ Temperature of the local Rindler horizon $\mathcal{H}$ from the Euclidean continuation
$⇒$ Virtual displacements of $\mathcal{H}$ allow for flow of energy across a hot horizon hiding an entropy $dS = dE/T$ as perceived by a given observer
$⇒$ The local horizon must have an entropy, $S_\text{grav}$
$⇒$ The dynamics should arise from maximizing the total entropy of horizon ($S_\text{grav}$) plus matter ($S_\text{m}$) for all LRF’s leading to field equations!
For more details and further references, see the review:

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*Padmanabhan, T. (2010). Thermodynamical aspects of gravity: new insights. Reports on Progress in Physics, 73(4), 046901, doi:10.1088/0034-4885/73/4/046901, arXiv:0911.5004.

