Which was the first movie with alternate ending?

The wikipedia page regarding alternate ending explained that:

In movies, alternate endings are often filmed before being scrapped, and may be subsequently included as a special feature in the film's DVD release. These alternate endings are a special type of deleted scene. In other cases, ideas that were presented but discarded early on are alluded to by the production team in commentary or interviews.

So, IMO a lot of movies might have alternate ending that maybe you are not aware of because it's not included in the DVD/VHS.

Let me explain better using Clue (1985) as example:

It is rare for a film to have true multiple endings, but one notable example is the movie Clue. Three different endings were used in the final version of the film (plus one unreleased fourth ending), with each having a different killer. This is a unique case in that the theatrical release had only one of the three endings, depending on the theater. For the DVD and video releases, all three endings were included, preceded by screen text such as, "That's how it could have happened..." The home viewer can either choose who he or she wants to be guilty, or the viewer can allow the DVD to choose randomly instead.

A fourth ending (where the butler did it all) was filmed but scrapped. Clue was orchestrated this way in part because it was based on a board game which offers multiple outcomes. The stage version of Clue also has multiple endings to a certain extent; the killer is randomly selected before the show. However, the true mastermind is always the same at the end.

So you can see, that the producer published deliberately all the endings. There could be other movies that have alternate ending, without a release.
But, searching around, IMDB helped me find a good track (not sure that's the best). There are some movies that are labeled as containing alternate ending, and the first (earliest) one is Scarface(1932).

I quote the wiki part that might interest you:

With the disapproval of several censors regarding the film, producer Howard Hughes, being wealthy enough to spend as much money as needed on the picture, willingly brought the film back to production by re-shooting an alternate ending.

The alternate ending differs from the original ending (version A), in the manner that Tony is caught and in which he dies. Unlike the original ending in which Tony Camonte escapes the police and dies getting shot several times, the alternate ending begins with Tony reluctantly handing himself over to the police.

Here's the wiki page of the movie. The producer however discarded the second version because the censors rejected it. This should be the first movie with alternate ending which we are aware of.

Hope it's what you were looking for.