Yes, it is possible to observe other galaxies while inside our own galaxy, the Milky Way. In fact, astronomers have discovered and studied thousands of galaxies beyond our own.
The visibility of other galaxies depends on several factors, including their distance from us, their brightness, and the level of light pollution and obscuring material within our galaxy. The light from distant galaxies can be affected by dust, gas, and stars in the Milky Way, making it harder to detect them.
However, there are regions within the Milky Way where the effects of obscuration are minimized, such as areas with less interstellar dust or regions away from the densest parts of our galaxy's disk. In these relatively unobscured regions, astronomers can observe more distant galaxies.
The exact distance at which galaxies become visible depends on the specific circumstances and the sensitivity of the observation equipment used. Generally, the further away a galaxy is, the fainter it appears. Telescopes, both ground-based and space-based, have allowed us to detect galaxies at immense distances, billions of light-years away.
It's worth noting that the study of galaxies is a vast field, and astronomers employ various techniques to detect and observe them, including optical telescopes, radio telescopes, and telescopes observing other wavelengths of light, such as infrared and X-ray. These instruments help us explore the universe and gain insights into the nature and evolution of galaxies, even from within our own Milky Way.