Also it depends on whether you're asking for the first demo games (as illustrated above) or more full fledged releases.
For instance, the old gamemaker.nl website had some good showcase games.
I don't know if it's among the first, but Seiklus was one of the first "big" GM releases I ever came across. It's from 2003, but even then, GM had already been around for a good while, so it's likely that something came even before that. It all depends on how you look at it, since it had to have had some sort of release in order for us to even know about it.
As with the others, not sure if it was the very first, but I remember Super Snake by Sander Steenhuis which I believe was 2002? You can still find a lot of these old games (I hope a link is okay). Doomed was also a good one that used a 3rd party 3D rendering DLL before GameMaker had 3D capabilities. Don't know the date on that one, though, but I remember it from around the same time.
Mark Overmars, a computer scientist, developed the program (Animo) that would become GameMaker when he was working at Utrecht University I believe. It is claimed in a 2009 interview that he developed the tool to get his children interested in computer science. He also taught game design courses in which a more robust version of GameMaker was used by students. It's a safe bet that the earliest games made with the tool were by Overmars' students or his children, if we aren't counting the man himself.
This all depends what you mean by "GameMaker" and "game". The GameMaker we use to day is a vastly different beast from the GameMaker that existed before YoYo Games acquired it. It's also very different from Animo. The creations people made with earlier versions of GameMaker would have been fairly limited.
You might ask: what was the first complete game created in the first public version of the GameMaker engine, and released to the community? Well, we could answer that question if we had access to "pub58.ezboard.com/bgamemakercommunity", the first ever GameMaker community promoted on Overmars' website (gamemaker.nl which now redirects to YoYo). Unfortunately, this has been excluded from the Wayback Machine, so it might not be possible to find anymore.
You can click here to read about some of the early games developed with GameMaker back in 2002 - 2003, but the links and images are broken for most, although page 6 has some screenshots including an early attempt to create 3D experiences with the engine (image above).
On topic though, I don't think I can say more than what's already been said. The very first game(s) made with GM are likely undocumented or lost. Back then GM and the whole idea of making a game on your own was still a new idea, so the first "games" were probably demos and small unfinished projects.
It gives you an idea of the possibilities of Game Maker 4.3 which was released in 2002. It is a very good guide. It is an updated version of the guide Carl Gustafsson made for Game Maker 4.0.
I myself started on Game Maker in 2002 with Game Maker 4.2a and at that point in time I got hold of Carl Gustafsson's guide for Game Maker 4.0 and later the same year Game Maker 4.3 came out and Carl Gustafsson updated the guide so it worked for Game Maker 4.3. I got that one too. The guides were available as PDF files and they were free downloads. I regard those guides as master pieces.