How long in gametime...

[SpecialK (OP)]

I'm feeling like the beginning of the game involves a LOT of mashing of the 30 day button, so I'm curious how long these things take in gametime for more experienced players. . . 

So, how long. . . 
. . .  until you have your first extrasolar colony?
. . .  until you have secured an adequate supply of minerals on your colony world?
. . .  until your first serious warship?
. . .  until you have > 30 or 40 labs?
. . .  until you expand your troops on your home planet?
. . .  until you can take on a precursor guard fleet (even a small/easy one) and win?

[Panopticon]

As with most things in the game, it rather depends on personal preference and the settings you chose when you started the game.
More information would probably be needed, are you doing a conventional or TN start? What is your starting population and resource points? And so on.

Except for the colony, you can get pretty much all of the things you listed at game start through managing the settings and SM mode.

[SpecialK (OP)]

I was using the tutorial settings.  So TM, 500 million, chose a bunch of basic techs, and no change to resource points (although I'm now pretty much out of resources in Sol, sadly, and there are no planets with a cost of less than 2 within the 4-5 jumps out that I explored, so the game's probably going to get reset when I get home from Xmas vacation. )