You're not the only one who has missed it, so don't feel too small!
It is common for a search form with a text entry field to appear by default on a site that supports search. In the case of SMF, though, most themes do not include a search form, but rather one must go to a secondary page to begin a search. It might prove to be trivial to add a search form in the header or footer area, if that was desired.
I suspect most folks who do not realize SMF supports search would notice the search capability if a form appeared by default.