I disagree generally with the "GA's are better in late game" argument.
GA benefits are spread evenly across empire, e.g. if they benefit a small empire "25%" they will generally also benefit a large empire "25%". Of course, 25% of small is less than 25% of large in absolute terms, but CIV is all about relative growth.
There are three arguments for early GA's:
- GA gives a benefit of +1h+1c on tiles already producing one of those. In early game, a cottage will go from 2c or 3c to 3/4c, an increase of 50% or 33%. In late game, the same cottage will go from say 6c to 7c, an increase of only 17%. The same for workshops, mines, etc. (Exceptions are of course tiles that get their first commerce or hammer, such as non-riverside windmills, US towns, and riverside levee tiles; so that is a consideration)
- In mediaeval times you get a number of new civic options, e.g. caste, bureau, OR/pac, HR. An early GA can let you adopt those civics without needing to waste turns to anarchy
- If you use an early GA to gain advantage, this can be multiplied exponentially. If it is true that most games are decided in the first 100 turns, shouldn't we use a GA in those turns?
One of my favourite plays is to use the artist from music to go into a golden age, run pacifism+caste during the golden age and max scientists everywhere. On the last turn, switch to whatever you really want to run. This way, you can exchange the artist for 2 or 3 scientists, which is a great boost towards Lib.
In general, a GA is a great time to do whatever your empire was not doing well. For example, if you are running a builder economy and you need to boost your unit output, use the GA to drop into military civics, build as many units as feasible, and drop back. Same for GPP as in the play above, or as a warmonger drop into tech civics to run towards a useful (military) tech.
I think the decision on whether you want a GA now are:
- is my empire growing population or am I around happy cap? If you are growing, a GA is less useful as it doesn't increase food
- do I have pending civic changes now or within the GA duration?
- how useful is the GP otherwise? Can it bulb or instabuild something useful?
- is there something important to gain from the boost? Will it give me a shot at important wonders? Will it allow me to win liberalism? Will it allow me to conquer an important piece of land? Maybe even: will it get my out of my REX hole and towards a good economy?