All right. I've been practicing, and still have not been able to have enough funds to build a trade port until at least 10 minutes in, if I'm colonizing everything in sight. Planet research, development costs, and extractors are just too much.
On my successful quick-expansion tries (which are extremely difficult for me to pull off perfectly), I was able to buy my first trade port at:
10 minutes / 5 planets (lots of metal, no crystal)
10 minutes / 6 planets (lots of crystal, no metal)
10 minutes / 5 planets (lots of metal, no crystal)
The limiting factor is usually crystal. Credits are never a problem.
I have two ideas to speed this up a bit:
(1) Sell more metal (if I see I'll have a surplus) and buy more crystal. At the moment, I'm always selling 200 metal at the very beginning of the game (at the peak price) and buying 100 crystal at its lowest point. But this is still not quite enough to get trade ports up ASAP.
Problem: selling resources at a discount and then buying resources at a markup results in a LOT of waste. Perhaps it'd be better just to wait another 4 minutes or so. Then again, what else would I be spending all my extra metal on? Or I could just buy a bit of crystal with my extra credits.
(2) Start completely skipping Volcano planets until a few trade ports are up, unless there are no other real sources of metal income. The cost of the first Volcano is 1600/375/300 (more than twice a trade port, after research) and at peak tax income is only worth about 1.6 trade ports, plus (usually unnecessary) metal income.
Another option is to restrict my colony frigate to only colonizing one planet initially (instead of 2), but I don't really like that idea much.
I'll try some of these and see what happens.