Yes, it was a terrible opening, but that's not all. The game took 30 turns, so, exaggerating maybe a bit, one could have even recovered from something like opening Curse/Copper if playing perfectly afterwards.
That said, let's look at your further turns.
Turn 5, maybe you want Gold over Goons given the fact you already have three terminal actions, but ok.
Turn 6: You don't need to use every buy you have. Even if that means you skip a whole turn. You did that right in turn 8.
Gaining two Coppers, only to buy Mint next turn to trash three coppers, well...
These two turns, you changed a Copper into a Mint (and got one VP token). Mint can be good, but not when your deck has 6 Copper, 2 Talismans and 1 Silver in a Colony game.
Turn 9: Rabble, another terminal action, even one that draws cards (and therefore will probably draw more actions dead)
Turn 10: Don't buy a Copper that early only because of one Goons played. Think about it this way: Would you gain a free Estate early on if you could?
Afterwards, it's not surprising you didn't get to 6$. In fact, it would be if you had regularly. How should you get to 6$ if your average draw is like two Coppers, two Actions of which only one can be played? Don't forget that you didn't really trash much of your starting cards at all, and you got some from your opponent's Ambassador, too.
Turn 21: You don't want a Trading Post at this point of the game, even if you got to play it next turn.
So, I hope that shows what could have been done differently, and that not the start only loses the game if the next 10 turns aren't that much better.