In General Relativity, matter curves spacetime, so instead of saying that all the “other fields” act within spacetime, perhaps “the metric [tensor] is determine

In General Relativity, matter curves spacetime, so instead of saying that all the “other fields” act within spacetime, perhaps “the metric [tensor] is determined by the matter and energy content of spacetime?” If geometry is described fully with a (tensor) field, perhaps we’re really just looking for a gauge theory but then that would be QM. Now I’m trying to imagine a tensor computing some infinite curvature supposedly necessary in GR.