With current technology, we could populate the galaxy in a few centuries. Slower-than-light ships establishing colonies on any habitable worlds they find, with colonies then sending out more ships as they reached the required level of technology, and so on.
If there are other intelligent species out there, they could do the same.
So far we haven't seen any of them.
Yeahhhh,,,, no. With existing technology we could not populate the milky way galaxy in a few centuries.
IF you have a speed of light spaceship, you will need around 1200 centuries to cross the Milky Way. And we milky wayans are living in one relatively small galaxy.
There are about 100 Billion other galaxies in the observable universe.
Yes, they are out there, and no, we will never find them.
Some of the theories that might be solutions:
Something notices when a race start moving around and sterilizes the area with a directed gamma ray burst/or killer robots. This is the berserker scenario.
They invariably fall into a virtual reality hole and never care about climbing out.
The drive to explore is actually a very rare trait among sapient life. So no one explores.
Once you get have tech to make reproducing probes you want them to be very quiet as well or maybe not even send them, because you don’t want to attract notice.
Freegards