How fast you can colonize depends on several factors, such as which race you use, which super ability and ability picks you use, what difficulty you're using, which races you chose as your enemies, etc...
I've been playing with an immense galaxy, Suicidal difficulty, 9 Major / 8 Minor (aka cash cows), as a custom race with the Iconian tech tree and Super Breeder ability. Abilities are 30% Econ(4p), 20% Moral(3p), 20% Research(4p), 10% Diplomacy(2p), 25% Luck(1p) and 25% Creativity(1p). Politically I go with the Technologists for another 20% Research.
The first techs I race toward (after Universal Translator) are for the Precursor Library, Interstellar Refinery, Molecular Fabricator, and the first 2 levels of miniaturization. Initial Colony has 14 production, added to IR's 16 for 30, then MF's 50% bonus for 45 production with just 2 buildings. CivCapital is 24, +16 IR for 40, +50% MF for 60 production on the capital. I build the PL, IR, and MF on every planet. Normally after I get those 3 buildings and miniaturization researched, I'll focus on Diplomacy and Trade techs, with misc others mixed in as needed.
I can make the initial colony phase last for anywhere between 100 and 200 turns on a immense / gigantic map, and about 80-150 on a large (run out of planets by then on large). Normally by the time the initial colony phase is over, sometimes while I'm still on the initial phase, I've started researching the hostile planet techs and will start the hostile planet colony rush.
During the colony phase, I don't build anything on the planets until they reach their population cap, except a starport (Since the starport has no maintence costs). They're all set focus to research until then. Once they're at 8 pop, I'll build the IR, MR, and PL, then 1-2 moral buildings and fill the rest of the slots with economy buildings or research buildings. If the PQ is higher than 20, I'll build a couple factories to speed things up. At this phase I only do either Econ or Research colonies. With about 100 colonies there will be 15-20 research focus and 80-85 econ focus. It's not until the other races start using weapons that I'll convert some core colonies into production so I can make ships faster. Even without converting colonies to production, I can still build tiny and small hulled ships within 2-3 turns with the IR and MR. I can always bribe a race not to attack me, so I'm not worried about building heavy defenses til my economy stabilizes.
Most of my ships will come from my home planet, normally at the rate of 1 ship a turn or every-other turn. At around turn 40 I'll start rush-buyng colony ships near the borders and use those to expand. After my home planet is filled with factories, I'll set the sliders split between military and research. Once I get the 2nd level of miniaturization, I can start building Tiny hull colony ships and save some costs there. When I get to the point that I want to start building each colony, while still maintaining the colony rush, I'll set the sliders to 1% military, and split the rest between social and research.
Typical game on a Gigantic / Immense galaxy, abundant everything:
*Turn 10 about 3 colonies.
*Turn 20 about 6 colonies.
*Turn 30 about 10-12.
*Turn 40 about 18-24. Start rush-buying.
*Turn 50 about 35-40.
*Turn 60 about 55-60.
*Turn 70 about 80-85.
*Turn 80 about 100.
*Turn 85 - Buy up all Economic / Research treaties from all 9 major and all 8 minor civs, as well as all the Extreme Environment techs they have. Research those techs for myself. The AIs are also just now starting to research weapons. Bribe each empire to attack eachother, as insurance they'll be too busy attack me.
*Turn 90 about 120.
*Turn 100 about 160.
*Turn 110 about 200 colonies. About this time there's no more colonies to colonize, so it's time to start building up each planet for war. I'm actually able to go upto turn 200 or sometimes well past turn 300 without building a single combat ship. And my home planet still only has Traditional Factories (Human) or Basic Replicators (Iconian) for production at turn 100ish.
All in all, I'm able to keep up with the AI in the colony phase, or sometimes out-colonize them, while having a Precursor Library on every planet helps to keep up with the research ends of things. The 'All-Labs' strat as I understand it is nothing more than building all labs and economy buildings once the colony rush is over, setting the production slider to 0/0/100 militay /social /research, and using the focus tabs on each planet to build military or social things.
