His special DNA is totally how he came back from being sucked into a black hole?
Regenerator G-1, if I recall correctly, is only Godzilla 2000 (which would include Godzilla 1954 for purposes of that continuity).
I mean, most of the time they didn't need an excuse. In the Showa series, he didn't really lose that much. The one in Godzilla Raids Again is another of the same species (or Gigantis, if you watch the stupid version). In the Heisei series, it was always something plot-related, because Japan had already identified and tried to exploit G-cells from pretty early on. Ocean temperature, time travel nuclear bomb, Rodan's surrogate sibling love for Godzilla's adopted son ...
I just mean, don't expect any familiar terminology, plot threads, or lore. We're in new territory with Godzilla Resurgence. Hopefully it does well in Japan and there will be more movies to come from Toho.