I haven't done all the research I should yet but just some logic before I get into researching organic growth vs synthetic.
So grow about .1 a turn at the beginning of the game so 20 turns to add 2 pop, I think in my last game with a synthetic race turn 1 it took 30 turns to build assembly on my homeworld, 25 on an Earth-like world or 39 on an extreme world, this drops to 9 for the Earthlike world or 13 on an extreme world if the production slider for the planet is maxed for manufacturing. However, when the organic races are building infrastructure their population also increases with the attending production increases, this is not the case for they synthetics, building population means not building more infrastructure during the whole assembly process and only gain the production increase when completed. While this might seem balanced because Synthetic races will quickly build up manufacturing and can devote the space organics would devote to farming to manufacturing, it is not. Early game is quite slow and while Synthetic races have higher population caps much earlier in the game this is another imbalance that needs to be addressed. Both need to be addressed because players will take ruthless advantage of it but the AI will not.
So my suggestions are as follows, first reduce the cost of the initial assembly by half, this allows Synthetic races to keep up with Organics, second bring Synthetic population cap down at the beginning of the game and build up their population cap more slowly, this slows down the players that will take advantage of high population caps to jump ahead while the AI is still struggling to keep up with the Organic races and still allow for high Synthetic population caps.