Unfortunately this appears to be unknown, but to date from some time in the 1930s.

It's quite difficult to pin down when the first "trailer" is from.

Straight Dope have an article where they quote Paramount executive Lou Harris, speaking in 1966, as claiming the first trailer was screen at an amusement park in 1912:

One of the concessions hung up a white sheet and showed the serial "The Adventures of Kathlyn." At the end of the reel Kathlyn was thrown in the lion's den. After this "trailed" a piece of film asking Does she escape the lion's pit? See next week's thrilling chapter! Hence, the word "trailer," an advertisement for a coming picture.

According to sites like Wikipedia (who reference the Nebraska Daily Star) and Hopes and Fears) claim the first trailer shown in a cinema occurred during a screening of The Adventures of Kathryn and was for a musical called The Pleasure Seekers.

Of course, there are a few problems with both of these examples. The Pleasure Seekers example is for a stage musical, not a theatrical film. It is arguable the Adventures of Kathlyn trailer is more accurate then, but it's not advertising a film either, just a serial.

And just as importantly - both of them were literally trailers. They trailed the film, appearing post-credits, not pre-credits as you've asked for.

Nevertheless I mention both here as they seem to have been a landmark moment in cinema.

There's precious little other information I can find from that era. Quite a few articles quote a 1914 New York Times article as stating:

“A committee of the National Association of the Motion Picture Industry yesterday began sending films known as trailers [advertising the bonds] to all of the 15,000 or more movie theaters in the United States. These films are seventy feet in length and will be attached to longer films that are shown at every performance.”

However, the majority of sites quote this as is, and the few that reference it appear to have broken links. Nevertheless, these trailers were still being shown after the main film.

At this stage, Wikipedia state Charlie Chaplin films had trailers created for his films from 1914, and cite page 53 of Blondes, Brunettes and Bullets by Nils T. Granlund. Whether this is believable or not is unknown.

In 1919, the National Screen Service was created, specifically to create and promote trailers. It was run by Herman Robbins, who opened an office, took movie stills, spliced in titles and informative text and sold them to movie theaters - all without the studios permission. Fascinatingly, rather than fighting this the studios praised it and outsourced almost all trailer creation work to them.

The NSS proceeded to dominate the trailer market for over four decades. During this time, they started making only trailers for silent films, such as the following trailer for The Live Wire:

Over time, they invented the first ever trailer with sound, for The Jazz Singer:

However, all of these trailers are still being showed after the films, not before.

Referring to the Straight Dope article again, they themselves refer to a book called Coming Attractions: Reading American Movie Trailers by Lisa Kernan, which is unfortunately behind a paywall. It apparently finds that the first trailers appearing before the film were invented around the 1930s.

Unfortunately, we don't appear to be able to narrow it down any further than this.

So in summary:

First ever trailer shown anywhere: The Adventure of Kathryn

First ever trailer for non-film shown in a cinema: Trailer for The Pleasure Seekers

First ever trailer for a film shown in a cinema: Unconfirmed, but allegedly a trailer for a Charlie Chaplin film.

First ever trailer for a film with sound: Trailer for The Live Wire

First ever trailer shown before the film: Unknown, but allegedly from a film in the 1930s.