No game update right now, but here's a description of all the mechanics of Golden Age and pop-booming in detail.
A population boom occurs when a base has a Growth modifier of +6 or higher. While that is true, the base will grow one population every turn as long as it has +2 nutrient surplus and is not at the habitation cap. The possible modifiers to Growth are +2 for Democratic politics, +2 for Planned economics, +2 for a Children's Creche facility in the base, and +2 while the the base is in a Golden Age. Note that the Hive faction's +1 Growth doesn't help; it is the only odd-valued modifier (there's no other source of +1 growth) and all the other modifiers and the target are even.
Most factions boom with the combination of Democratic, Planned, and the Children's Creche; and can do so automatically and indefinitely as long as they run those policies. The Hive and Morgan Industries can't, due to being barred from Democratic and Planned respectively. They each must use a Golden Age to make up for the missing SE component. A Golden Age occurs when a base of at least size 3 has at least half talents and zero drones. This is tricky to manage, and becomes impossible with too many bureaucracy drones.
First I'll cover the details of how psych works. Every 2 psych converts one content worker to a talent, or if there are no workers, converts a drone to worker. But there is a hard cap that psych is limited to a number of conversions equal to the base size, no matter what; psych multipliers and specialists cannot exceed this. If all citizens start as drones, a size-5 base does this with psych:
Notice that the Golden Age is impossible from psych alone. Only 10 psych can be used at a size-5 base; any beyond that is useless. The psych goes like this: 4 to convert the first drone up to a talent, 4 also for the second, then 2 for the third drone to worker... but that's it, we are not allowed to use any more psych to create a third talent. We can handle plenty of drones with police and recreation commons, but we can't get that critical third talent to get up to half.
The Human Genome Project is the only way to get that critical missing talent. With it, in fact we only need 8 psych instead of 10, to get two talents, then police and the HGP create the third.
That example is with one bureaucracy drone on Transcend difficulty, so that every citizen starts as a drone. If you go beyond that, the next b-drone converts one of those drones into a "superdrone". This is not obvious on the base psych screen; the superdrone icon is only slightly different than the regular drone, that slightly more intense red.
Superdrones get the first priority to consume psych; all psych converts them to regular drones before anything else. In this base, 2 psych first goes to fix the superdrone, then the remaining 8 creates two talents and the HGP the third. The Golden Age is still possible, although it's considerably more difficult for a Hive base to get 10 psych than 8, which is why I stopped expanding before this would happen.
With two superdrones, it looks like this:
Now the Golden Age is completely impossible. 10 psych first assigns 4 to two superdrones, leaving only 6 for talent creation, which is enough to get only one, and the HGP can make only one more with no means to a third. This effect will occur at all odd-numbered base sizes with two superdrones, and also at even sizes with a third.
More talent-creating facilities exist much later on the tech tree, but by that time there's the Cloning Vats secret project which gives a permanent population boom anyway. The Peacekeeper faction's extra talents also work to offset superdrones. The PKs don't need a Golden Age anyway since they can pop-boom with the usual SE settings; but it's actually an interesting possibility to pop-boom with Democratic+Planned+Golden Age and skip building the creches and perhaps even the HGP.
I use size 5 as the example here because that's the most critical number. Size 6 is just as easy to reach Golden Age as size 5, since that requires the same three talents. Size 7 is irrelevant because that's the habitation limit anyway. More generally, odd sizes are most challenging because you actually need more than 50% talents, and size 5 is the highest relevant odd number.
Besides the growth modifier, booming requires +2 nutrient surplus. It's quite aggressive to try to do this so early, before Gene Splicing and condensors and tree farms increase the food supply. A nutrient-bonus tile makes it easy to get up a few sizes, but any base without one can only boom as long as every worked tile yields +2 food. It can become necessary to use supply crawlers for just 1 food each on forest, and that will be my approach here for the most food-poor bases, rehoming them from food-rich cities.
One more important aspect: The Golden Age and the +2 nutrient surplus
don't have to occur at the same time. Each turn, the game first checks the current growth rating and nutrient surplus,
then checks for the base to exit or enter Golden Age status. A Golden Age begun on one turn lasts through the nutrient-production step on the next. A base can work a configuration with enough psych (perhaps doctor specialists) to enter Golden Age on one turn, then on the
next turn switch to a +2 food configuration and boom even if that drops it out of Golden Age. This obviously takes longer than maintaining both the GA and +2 food in parallel, but sometimes that's not possible at bases with limited access to food and energy.