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you're tripping dude. you have it 180 on reality.
In galactic timescales, i.e. 13.8 billion years until now, there is plenty of time for colonisation of an entire galaxy - for instance, our galaxy. There have been several very simple mathematical models that suggest even at very modest transportation speeds of 0.25% of the speed of light, galactic colonisation across a radius of 120,000 light years (our galaxy) could be easily achieved in like 500,000 years.
basically nothing on the galactic timescale
http://www.sentientdevelopments.com/2012/01/new-mathematical-study-reveals-that-our.html
for example
At 0.25% c, it would take 500,000 just to travel across the galaxy, not colonize it.