Looks like I might be under estimating the delay. From an article from Pete Vilmur, the first dated photo with the poster in a theater is from late July!
The Style A poster may have actually been a no-show on opening day. Considering the timeline suggested by the addition of the droids described above and the photographic record of the day, it seems very likely that the famous Jung artwork poster was not available for the May 25 release. In fact, the earliest published photo of the poster itself to come to light in the Lucasfilm Archives is from July 27, over two months after the release on May 25
https://www.starwars.com/news/7-things-you-didnt-know-about-the-original-star-wars-poster
