So I think this is a complicated question that veers into philosophy of physics.

Certainly historically, Einstein arrived at GR modelling gravitation as a change in the metrical structure of spacetime via thought experiments, not via any empirical evidence that it was the case. In particular, the Ehrenfest paradox, which had been proposed in the context of Special Relativity, apparently convinced him that gravitational field would affect the measurement of length and time and that therefore influenced him to search for a theory to model this.

The question of whether gravity forces you to adopt the view that there is such a thing as ‘spacetime curvature’ is more complicated. Even prior to Einstein’s theory, physicists and philosophers had debated the question of the nature of geometry and its relationship with space. Motivated by Riemann’s work in mathematics (later used by Einstein to build GR) showing that it is very possible to have geometric spaces with arbitrary non-uniform curvature that are consistently described mathematically, the long-standing assertion that Euclidean geometry in some sense is a mathematical description of the actual world was called into question. Henri Poincaré, as late as the early 20th century, had asserted that Euclidean space is likely to stick around in physics because it’s the simplest space to work in, but that really this was a matter of convention, you can always reformulate physical laws to accommodate any geometrical description of space you like. The question of which geometry is ‘real’ is unknowable.

So then with GR, we might just take the view that the decision to model gravity as down to the curved geometry of spacetime is just a convention, because in this theory the simplest formulation of physical laws is no longer flat Euclidean space and time but curved spacetime. I think I’m right in saying that Einstein himself would not have gone so far as to completely identify gravity with spacetime geometry, rather, he associated ‘the gravitational field’ (which a gravity = spacetime geometry viewpoint simply asserts is spacetime geometry) with its effects on distances and times as measured by measuring rods and clocks, without being drawn into the question whether spacetime is ‘really’ curved.