Okay, let's do some quick math, to disprove your bullshit again.
The Milky Way has 100–400 billion stars in it.
The average distance between stars in the Milky Way is 5 light-years.
So, 5*100,000,000,000=500,000,000,000 light-years, and that's the lower-band estimate.
The earliest life could have existed in the universe, it thought to be, at the maximum, for carbon-based life is 1-to-1.5 billion years after the Big Bang. Which is, at the very best, 12.8 billion years ago.
Which means, even at the very best estimate, if complex life had started colonizing the Milky Way as soon as they started existing 12.8 billion years ago, they could have only gone 12.8 billion light-years.
Which means, they still have 487,200,000,000 light-years to travel, before they will have colonized the entire Milky Way.
So no, you're still wrong. We'd still have plenty of stars, even with me being overly generous and giving your theory the BEST odds possible.
Once again, you're an idiot, stop spouting this bullshit theory.