If both these galaxies are on collision path because of their gravity but how could that be?
They are 2.5 million light-years apart now but I imagine they are still n collision path for a long time and the universe is 14 billion years old.
Does this mean they could be 20 million light-years away at some point yet their gravity started to attract each other?
I can't see where you get 20 million light years from. They are 2.5 million light years apart now, and will collide in about 5 billion years time. This suggest perhaps that when they formed around 12.5 billion years ago, they might have been, at most, 9 million light years apart.
Both galaxies are of mass $\sim 2\times 10^{42}$ kg. If they were 9 million light years apart, then each would feel an acceleration of about $2\times 10^{-14}$ m/s$^2$. Even were that acceleration to stay uniform (it of course increases as $1/r^2$), they would cover half the distance between them in just 70 billion years. Thus merger on a timescale of about the current age of the universe is not unexpected.
A more general way of thinking about it is in terms of the typical gravitational dynamical timecscale $\tau \sim (G\bar{\rho})^{-1/2}$, where $\bar{\rho}$ is the average density of a structure. The local group of galaxies is dominated by Andromdeda and the Milky Way, and is about 10 million light years across and contains about $5\times 10^{42}$ kg, so $\bar{\rho} \sim 10^{-26}$ kg/m$^{3}$ and $\tau \sim 40$ billion years. Again, this suggests a merger after $\sim 16$ billion years of evolution is not unexpected.
they could be 20 million light years away at some point yet their gravity started to attract each other?
Gravity has infinite range. It gets weaker and weaker as you go further away, but there isn’t a cutoff point where it goes to zero. It’s an “inverse square” law and $1/r^2$ is nonzero at arbitrarily large $r$.
We don't actually know that Andromeda is on a collision path. It is coming closer, but in the absence of an accurate determination of proper motion, that does not imply collision. Gravity cannot (on its own) explain the observed randomness in peculiar velocities of galaxies. Galaxies were formed from gas clouds. The conclusion should be that peculiar velocities already obtained in the initial conditions of galaxies formation. This is natural since one expect high velocities to be generated is gas in the conditions of the big bang. I have considered this in some depth in The effects of turbulence generated in Big Bang nucleosynthesis
