It will overflow at
System.out.println(new Date(Long.MAX_VALUE));
which prints
Sun Aug 17 03:12:55 GMT-04:00 292278994
That’s thus after a bit more than 292 million years. I’d say, there’s a plenty of time to invent a solution in the meanwhile. To be honest, I don’t expect the humanhood to survive this. We exist only a few seconds as compared to the age of the world in hour scale and it won’t take long.