The universe is about 14 billion years old. The Milky Way is about 13 billion years old. Our solar system is only about 5 billion years old.
If intelligent life appeared elsewhere in the galaxy as well, perhaps many times, it probably happened many billions of years ahead of us.
Ergo: unless all civilizations die off for some strange universal reason, the galaxy is already colonized by others (or their robot descendents). (I doubt you need more than a billion years to colonize the entire galaxy, even without faster than light spacecraft.)