Our galaxy, the Milky Way, is estimated to be around 13.6 billion years old. This age determination is based on the age of the oldest known star clusters within the Milky Way, as well as the age of the universe itself as determined through observations of the cosmic microwave background radiation.
Regarding galaxies older than the Milky Way, it is challenging to definitively identify individual galaxies' ages due to the limitations of current observational techniques. However, based on current understanding, it is likely that there are galaxies in the universe that formed earlier than the Milky Way.
Some of the oldest and most distant known galaxies observed by astronomers are seen in the Hubble Ultra Deep Field and the Hubble Extreme Deep Field images. These images provide a glimpse into the universe's past, showing galaxies as they appeared when the universe was much younger.
The estimated ages of these early galaxies range from about 13 to 13.8 billion years, which is roughly comparable to or slightly older than the age of the Milky Way. These galaxies are located at vast distances from Earth, with light from some of them taking billions of years to reach us. The precise distances to individual galaxies in these deep field images can be challenging to determine accurately, but they are typically billions of light-years away.
It's important to note that our understanding of the universe is continually evolving, and as observational techniques improve and new data is gathered, our knowledge of galaxy formation and age estimates will become more refined.