Yes, something that we have created already left the Milky Way Galaxy; it might have even reached Andromeda Galaxy, 2.5 million light-years away and 59 currently known satellite galaxies of our home galaxy.

Our galaxy has a diameter of about 100 000 light-years and contains 200 to 400 billion stars. For something to leave it, it has to achieve an escape velocity of 550 km per sec/340 miles per sec. There are some ways in which, naturally, something can leave our galaxy at these speeds.

• Some satellite galaxies pierce the disk of our galaxy during their orbit and come out on the other side if they are near enough and their trajectory is vertical to the spiral. They can repeat this trick a few times before they get absorbed.
• Previous mergers with massive galaxies, like the one that occurred 8 to 11 billion years ago with Gaia-Enceladus Galaxy that added about 50 billion stars to our galaxy, or interactions with the satellite galaxies lead to some systems, planets, or other smaller celestial objects to be flung out with required escape velocities.
• Within galaxies, stars don’t have the same speeds and directions of movement. Some approach each other quite close sometimes. It rarely happens in our corner of the Milky Way, where the density of stars is low, but in some denser clusters of stars and the central bulge, it happens more frequently. Such approaches can cause systems or objects in systems like planets to acquire escape velocity from the galaxy.
• Supernova explosions can cause partner stars in multi-star systems or planets to acquire even up to 0.375% of the speed of light and leave our galaxy.
• Hypervelocity stars, planets, or smaller objects can achieve up to a staggering a third of the speed of light if they are freed from multi-star systems that interacted with black holes or especially supermassive black holes in the center of galaxies.
• Rogue stars, planets, and smaller objects from outside our galaxy can pass through it and leave eventually; they can be affected by the gravitation of our galaxy, and their direction of movement might change.
• Various forms of radiation from within our galaxy or outside leave the Milky Way at the speed of light or charged particles at speed close to the speed of light. Their trajectories are affected by gravity, and in the case of charged particles, they can also be affected by the magnetic fields inside our galaxy.

Homo sapiens have existed for 200 to 300 thousand years. The nearest satellite galaxies are tens of thousands of light-years away, and some stray photons of our artificially created fires have already reached such distances. The Andromeda Galaxy is 2.5 million light-years away. Although homo sapiens haven’t existed for 2.5 million years, the idea of what it is to be human is blurred.

We evolved from a long line of human-like ancestors that already cooked food for hundreds of thousands of years or longer, and the first fires that our foremothers and forefathers artificially started might have been two to three million years ago.

This means that some photons we fabricated through our technology might have already reached the Andromeda Galaxy by now.