The universe is far too big. I mean its really really big. Even if we acquire FTL, lets say in the next decade(for assumption's sake) and start traveling. Its possible given our resources, time and required focus to achieve anything meaningful we may not even step out of milky way for several thousands of years from now.

The milky way has around 100 billion stars. Searching 100 billion stars for some meaningful results is not a Joke. Even if we do divide and conquer or do the equivalent of map-reduce approach to exploring space. There is no way we can get to meaningful results even in several thousands of years from now.

There fore the biggest challenge after the invention of FTL will be how quickly we can multiply spread and explore.

Trust me once we get FTL technology, the biggest challenge will be the dealing with overwhelming size of universe. In fact just within a few years we may even think FTL was an easy problem to solve. Our problems will be exploring the universe within human life timescales, multiplying fast enough to occupy and explore it.

So an alien civilization in some really far galaxies even with FTL technology possibly cannot search for us in the size the universe is.