It’s well understood that the expansion of the universe is not “due to general relativity”. General relativity does explain some details of that expansion.
The expansion of the universe is largely due to the impulse provided by the Big Bang. General Relativity does attempt to explain some details regarding what’s happened after the Big Bang, but provides no insight into the Big Bang itself. Nor does it offer insight into Dark Energy, a concept that Einstein opposed.
The universe is expanding due to general relativity... in the sense that Einstein literally wrote "... plus the expansion of the universe" into his equations.