There are billions of stars in the galaxy that are similar to the Sun, many of which are billions of years older than Earth.
With high probability, some of these stars will have Earth-like planets, and if the Earth is typical, some might develop intelligent life.
Some of these civilizations might develop interstellar travel, a step the Earth is investigating now.
Even at the slow pace of currently envisioned interstellar travel, the Milky Way galaxy could be completely traversed in about a million years.
The problem with notions such as these is they leave out inconvenient variable.
Humans (defined as creatures capable of using fire and cutting tools) have existed for at least 4.5 million years. While life has existed for almost 2.5 billion years.
99% of human existence we lived a feral existence. Changes to our lifestyle during that 99% of our existence were minimal.
In the last 1% of our existence numerous civilisations, large and small, many deeply ingenious have come and gone.
Yet it is less than 250 years ago, that one, quite small, and relatively insignificant civilisation has developed the entire modern world.
Add that negative variable and the so called paradox become somewhat less interesting.
Then add on the variables of incentive. For what reason would a civilisation, want to traverse the Milky Way?
For what reason would such a civilisation choose to visit here?
Given the enormous number of angles which such a trans Milky Way exploration, what are the chances a million of these might happen to cut through the Solar System?