Unfortunately, the only way to do that with Java 8 is with the solution provided by Holger.
However, the operation dropWhile(predicate) has been added to Java 9 so starting from JDK 9, you can simply have:
Stream.of(0, 1, 2, 3, 0, 1, 2, 3, 4).dropWhile(n -> n < 3).forEach(System.out::println);