JSON generally requiring the entire document to be present before parsing can indeed be a problem. However, for one common use case there is a pseudo-standard, namely "JSON lines".

"JSON lines" extends JSON by a) not allowing newlines in values and b) allowing newlines to be used as a top-level separator for elements of a list, instead of the JSON-compliant comma-separated list enclosed in square brackets

This allows for per-line parsing, which can significantly reduce memory usage and allow for partial parsing in some scenarios. I've seen it used where the data is fundamentally a large collection at the top level where producing proper JSON was using too much memory