Was there a Die Hard movie poster that excluded Bruce Willis?

There is an episode of the docu-series The Movies That Made Us (a spin-off of The Toys That Made Us) that is about the making of "Die Hard".

Writer Steven E. de Souza had this to say about the audience reaction when the trailer hit theaters:

... when Bruce Willis came up, the audience laughed ... some people even said they weren't just laughing at the trailer, they were booing ... so, the studio was in a panic.

And director John McTiernan commented:

They took him off the poster about a month before the movie came out.

So the studio made a poster featuring just the building.

Only after the movie proved to be a box office hit, did they put Bruce Willis' face back on the poster.

^{[both images are screenshots taken from the docu-series]}

Following up on the answer by @Oliver_C I've managed to find that ads lacking Bruce Willis were indeed featured in newspapers. For example, here's a clip from a The Journal News on July 12th 1988:

Similar ads were posted on July 12th-14th by The Miami News, The Record, The Philadelphia Enquirer and The Daily News. These newspapers had a version of the poster that mentioned 70mm film and Dolby Sound:

This was noticed by newspapers at the time, as evidenced by this short article in The Press Democrat on July 14th 1988:

After paying Bruce Willis a reported $5 million to make "Diehard." 20th Century Fox is choosing to make little of his name in promotion of the picture. TV spots make the movie out to sound like a thrill ride at an amusement park; while one has to look through the fine print at the bottom of the page to see any mention of Bruce's name in newspaper ads that scream "On July 15 ... An Adventure That Will Blow You Through the Back Wall of the Theatre."

However the ad for Die Hard in the LA Times on July 15th 1988 did have Bruce Willis in it:

Given that the red-carpet premiere occurred on the evening of July 12th 1988, it seems that the producers have decided to include Bruce Willis after all sometime around July 13th.

It's not that he was excluded, but given he was only seen as the comedic character David Addison in Moonlighting the studio was possibly nervous about featuring Willis.

The poster you ask about is this:

As you can see the Nakatomi building is as important, showing the action which people might not assume from a picture of Willis. There is also heavy description to ensure people realized it was a thriller.

As word spread as the film went around the world (remember the days when films didn't open everywhere at once) Willis became more the key factor (and later films followed this style)