Einstein solved three very different open problems in one year: the photoelectric effect, Brownian motion, and special relativity.

Others may have gotten close to one of these solutions, but nobody else came anywhere close on all three.

General Relativity as his own research programme was designed to capture the consequences of constraining the speed of propagation of changes of gravitational influence; it was literally about relativizing gravity. GR was not designed to explain Mercury specifically (or even really motivated by Mercury), the theory just happened to explain why its orbit traces out a daisy-like pattern rather than a perfect ellipse. GR also correctly predicted a deflection of background starlight around the limb of the sun (1919 eclipse and eclipses since), stellar gravitational redshift (Sirius-B initially, many many objects since), and gravitational redshifts induced by Earth (all reliable results were posthumous: Pound-Rebka and similar since 1959, and more recently precision lunar and satellite ranging).

Indeed, Einstein liked to explain that his mental toy in understanding relativistic gravitation was someone jumping off the roof of a house, or the behaviour of things (e.g. flashlights/torches) riding in office-tower elevators/lifts (which date from the 1870s). That's a far cry from precision measurement of Mercury's perihelion!

There were no real astrophysical or terrestrial problems calling out for General Relativity. Even after General Relativity was a published theory, real gravitational problems were solved with low-order correcting terms to Newtonian gravitation and with linearization: an approach which Einstein practically invented, and which he used himself when thinking and writing about early problems in cosmology (the discovery of Cepheid variables opened up a lot of those).

There were quickly alternatives to General Relativity which predicted some but not all of these early classical tests of the theory. Eddington's 1922 book was the first shot in a body of literature analysing different theories of gravitation and how they differ in their predictions of dozens of tests of General Relativity. Will's work in particular is useful: https://en.wikipedia.org/wiki/Parameterized_post-Newtonian_f... -- you can see how it's used in practice in this open access paper https://www.nature.com/articles/s41467-017-02558-1

That said, there are mathematical tools available now that weren't available to Einstein in the early 20th century, and he might have chosen to arrive at a different (but equivalent) formulation of General Relativity. The standard Hamiltonian and a variety of modern Lagrangian formulations are particularly useful, and it could have been nice to have had <https://en.wikipedia.org/wiki/Initial_value_formulation_(gen...> before the 1960s (even though it arguably only shines brighter when you have 21st century supercomputers).

Indeed, one can imagine Einstein starting with Lie theory, such that Special Relativity from the start is just the theory of spacetime with SO(3,1) symmetry at every point. But Cartan, Killing, and Noether came decades later and were motivated by Einstein. And quite a bit of group theory developed as the Standard Model developed after Einstein was already dead (notably Goldstone's theorem, 1960s). So to first formulate General Relativity as a GL(4,R) group theory with spontaneous symmetry breaking to SO(3,1) one would need to rearrange an awful lot of physics history.

Any of these alternative-universe mathematical origins would just have been using different tools to arrive at the central result: we inhabit a Lorentzian spacetime in which there is an exact matching of moving matter and a metric tensor (at each point in spacetime) encoding durations, spatial lengths, and angles, or the equivalent set of orthonormal vector/covector fields.

And worse, the physical content of the theory -- however formulated -- probably would still have been considered interesting but practically useless until the 1970s.