This is misleading at best. The JVM only exposes multibyte values to ordinary applications in such a way that byte order doesn't matter. You can't break out a pointer and step through the bytes of a long field to see what order it's in, at least not without the unsafe memory APIs.
In practice, any real JVM implementation will simply use native byte order as much as possible. While bytecode and other data in class files is serialized in big endian order, it will be converted to native order whenever it's actually used. If you do pull out the unsafe APIs, you can see that e.g. values are little endian on x86(-64). The JVM would suffer from major performances issues if it tried to impose a byte order different from the underlying platform.
One relatively commonly used class which exposes this is ByteBuffer and its Int/Long variants, but there you can specify the endianness explicitly (or set it to match the native one).