So there are 2 places the event triggers depending on what game version gog has:
1. By the Supermart infested with Raiders early in game that is tied to a mission. You'll hear a sonic boom then see green vials lying around in the parking lot and towards the underpass of the destroyed bridge overhead. [sometimes the blaster gets trapped on the bridge]
2. You follow the alien distress call in the desert and find a crashed ship and get it from a dead alien in a cave along with 100+ scattered ammo cells

xbox 360 is the later version. Whose found the blaster and where?

I know about the one place only. And the Alien Blaster is always found there. A crashed flying saucer appears in one of the random encounters. And you can pick the Alien Blaster from one of two alien humanoid corpses near that saucer.

It's the latest PC version.

I haven't played the GOG version of FO3 yet, though I do own it. My playthroughs were from the retail pc version.

But I do know in that version, if I saved far enough away, I could cycle through the random events, eventually getting the alien blaster and some ammo.

One place was the supermarket area. The other was a barn that was close to the starting shelter I think.

There are other places of course, but those two I had a pretty good idea of where to save the game to reload in case the event I wanted didn't happen.

Doing this, I was able to get the alein baster and a decent amount of ammo (they were scattered, so the recovered amount varied) in one location and the nuke launcher in the other area or vice versa.

The easiest ofc is transitioning from map to map, from underground to above ground for example. This made it easier to trigger the random encounters, but I don't recall where these places were now. It's been too long. Only the lwo listed above I'm 100% sure off, since I reloaded enough ttimes to get the blaster lol.

So back when I played it, you could reload to get different random events, though some seem to show up only in certain areas.
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Ahh the aliens. On the one hand, I love the bizarre space adventure DLC as an experience unique in the game, and heck the aliens "fit" the 1950's retro futuristic setting well enough.

BUT, it doesn't fit the themes of the game, or the series as a whole, to imply that aliens are responsible for mankind's woes. We did it to ourselves and to suggest aliens are the cause of the divergence between this reality and our own is... well I'm not the first not to like it.

All that's okay though. When I pop out that alien blaster or go to find that distress signal, my head cannon is that my character is hallucinating a sequence informed by all the sci-fi stories e read growing up in the vault. The characters all seem content to stay inside this little campaign rather than go out into the world, so the story stays nice and self contained. It's escapist fantasy, a way to pretend if only for a moment that these horrors have someone else to blame. Then, when it's all over, they wake up. Return if they like, the comforting fantasy will be there to greet em again.

The blaster? The craft? The gel? Maybe it's actually alien, maybe they're Russian or Chinese tech, or maybe they're just another hallucination and the rest of the wasteland sees something more mundane compared to the wanderer.