[another_someone]

As I understand galactic evolution, most star birth (or is it all star birth) happens on the edge of the galaxy, which in a spiral galaxy such as ours, means in the arms of the spiral, which is where we are.

That means that at some time in the past, other stars that were once on the periphery of the galaxy, such as our Sun, became part of the main body of the galaxy.

How like our Sun would these stars have been, or do stars like our Sun just not live long enough to reach the core of the galaxy?

[DoctorBeaver]

The long-standing belief, which is now backed by observations, is that galaxies begin their lives as small spirals that gradually evolve into larger, elliptical galaxies.

As for how the individual stars behave, I do not know if there is a consensus of opinion.

I don't see that stars such as our sun would exist long enough to migrate close to the centre of the galaxy. Ours is 4.5 billion years old and is still much closer to the edge than the centre.