How do I get the first element while continue streaming?

If your starting point is a Stream and you want to retain all of its properties and the laziness, the following solution will do:

public static <E> Stream<E> forFirst(Stream<E> stream, Consumer<? super E> c) {
    boolean parallel = stream.isParallel();
    Spliterator<E> sp = stream.spliterator();
    return StreamSupport.stream(() -> {
        if(sp.getExactSizeIfKnown() == 0) return sp;
        Stream.Builder<E> b = Stream.builder();
        if(!sp.tryAdvance(b.andThen(c))) return sp;
        return Stream.concat(b.build(), StreamSupport.stream(sp, parallel)).spliterator();
    }, sp.characteristics(), parallel);
}

E.g. when you use it with

List<String> list = new ArrayList<>(List.of("foo", "bar", "baz"));
Stream<String> stream = forFirst(
        list.stream().filter(s -> s.startsWith("b")),
        s -> System.out.println(s+" ("+s.getClass().getSimpleName()+')')
    ).map(String::toUpperCase);
list.add(1, "blah");
System.out.println(stream.collect(Collectors.joining(" | ")));

it will print

blah (String)
BLAH | BAR | BAZ

demonstrating that the processing will not start before commencing the terminal operation (collect), hence reflecting the preceding update to the source List.

There is StreamEx library that extends standard Java's Stream API. Using StreamEx.of(Iterator) and peekFirst :

StreamEx.of(itemIter.iterator())
        .peekFirst(e -> System.out.println(e.getClass().getSimpleName()))
        .forEach(System.out::println);

Native solution: Stream in Java is not reusable. This means, that consuming stream can be done only once. If you get the first element from a stream, you can iterate over it one more time.

Workaround would be to create another stream same as the first one or getting the first item and then creating a stream, something like that:

Stream<E> stream = StreamSupport.stream(Spliterators.spliteratorUnknownSize(sourceIterator, Spliterator.ORDERED), false);
E firstElement = itemIter.next();
stream.foreach(...);

Edit

There is not really any way to "copy" a stream, you need to keep an iterator / collection. More about it here. When it comes to memory once stream is exhausted, it can be collected by garbage collector as there is no use from it. Stream itself does not take more space than iterator it originates from. Bear in mind, that streams can be potentially infinite. Elements currently manipulated are stored in memory.