Galaxy orbital momentum early on would not necessarily mirror the one they have today, since they have merged so many times. The Milky Way seems to hold the ghosts (star clusters) of many dwarf galaxies and gas clouds, that each contributed their own momentum.

But more generally when galaxies started to form around dark matter filaments caused by quantum fluctuations during inflation, they did so against a much more heterogeneous background. Seems the first stars formed where gas was chaotically aggregated to 1000 times the average density at the time. explaining why they formed early but at low numbers.

So, gas chaos in density and momentum, with totally random gravitational seeds, due to quantum fluctuations of a previous era. Not a picture that makes one expect spin correlations. Though I assume people have looked, but not reported any result deviating from zero correlation what I know of.