Not certain how either of those actually initiates a golden age. Paucity of examples in mods I've looked at and in the wiki make me puzzled about the parameters.
"Player:ChangeGoldenAgeTurns(int change)" seems to me to have to do with the length of a golden age, not the occurence of one.
"Player:ChangeGoldenAgeProgressMeter()" has no examples in the wiki and does not say what the parameters are. My guess, something to do with how soon a Golden Age will occur.
Player:GetGoldenAgeProgressMeter() and Player:GetGoldenAgeProgressThreshold may be used, but again, the wiki does not show them in use except in toppanel.lua.
Player:SetGoldenAgeProgressMeter() may be useful but I've no examples of how to use it.
I'll continue to look, but I may have to add it via a wonder. I was hoping to have a golden age initiated when a certain Project was finished, this done by lua.