Think about this
What if intelligent civilization exists only 1 per galaxy. That would mean there are 2+ trillion ETs out there ....only problem is we'll never be able to communicate with each other and/or see if the other exists
Not only that... you're not thinking 4th dimensionally.
For example, humans have only been around for 250,000 years. And of that period, we've only been capable sending communications beyond our earth's atmosphere for about 0.0004% of that time. It's also hard to say how long will the human civilization survive. We might just be here for another 50,000 years or so before a massive Ice Age, meteor, or worldwide plague wipes out mankind.
Our time on this planet might only be about 300,000 - 500,000 year window. So if there is other intelligent life out in the galaxies, they would have to develop communication/space travel during the same window of our existence. Considering the universe is billions of years old and will be around for another billion years, add this with the size of our universe, the chances of us encountering other intelligent life during our human timeline is very minute. The longer human civilization survives, the better chance we have of encountering alien life. But humans would need to survive for hundreds of millions of years (with space communication/travel ability) to have a chance at actually encountering other intelligent alien life.
But considering how much human civilization has changed and how much we've changed the planet in just the last 100 years, it's impossible to fathom what we or the planet will look like in a million years, let let alone the next 50,000 years. Also in a normal human lifespan of 75 years, the chances of an extinction level meteor event is extremely low. But once you start talking on the scale of million years, an extinction level event is pretty much guaranteed to happen. The challenge for human civilization is to perfect space travel, so when the extinction event does happen to planet earth, we've already colonized other planets to ensure our continued survival.