There are billions of Suns in the galaxy. All the objects in our system besides the Sun were orbiting some other star before they were adopted by the Sun, or even by their hosts, such as Saturn and Jupiter with their multiple moons.
Yes orbital captures would take a long time too. This theory is a completely different worldview in almost ever regard.
Just to keep things in perspective, 1 light year is about 6 trillion miles. At Earth's orbital velocity around the Sun, at 66,600 miles/hour, it would take about 1 million years for Earth, assuming it was flung out of its orbit by another more massive body passing by, to reach any object within 100 light years of our current position. There are many, many objects in a sphere of 100 light years. As well, this means there should be many millions of objects freely floating that are Earth sized and bigger/smaller that are going to be adopted by younger hosts, and are experiencing mass extinctions on their surface as we talk about this!
The question then could be asked, how long does an extinction last for? Because as far as I can tell, it would last for quite a long time. In that period Earth flying through outer space would become ice cold and also slam into lots of asteroids while clearing a new orbit with another star. An iceball Earth would decimate a very large portion of life. Not only that but regular orbit changes over very long periods of time would explain the mass extinctions, and why they occur in different intensities and over tens of millions of years. https://en.wikipedia.org/wiki/File:Extinction_intensity.svg The salinity of the oceans would change, the amount of water on the surface would change, the chemical composition and abundances of elements in the atmosphere would change, etc.
The belief that Earth has always orbited the Sun is also problematic for other reasons, such as the Faint Young Sun paradox. https://en.wikipedia.org/wiki/Faint_young_Sun_paradox
Water was on the Earth's surface before the Sun was able to keep it liquid. Of course this can be explained in GTSM, the Earth formed its own water for one, it is vastly older than the Sun two, three it has orbited other stars in its past. So we are dealing with here is a completely different worldview