1) Free services (this has been ruled out as an option - although you could still do some now and then on weekends, maybe?)
2) Buying GP at higher than the main buyers/sellers and selling lower to break even but build trust.
3) Player auctions offers more security to buyers and so might be a better option
4) Find a friend or someone who can help you out and start some sort of business (questing/kiln cape/etc). You'd have a second person to help you out, more time commitment between the two of you, and you could build trust faster.
5) Donating/Sythe Verified/Post Count are also ways to build trust.
6) Stay active over time. The more active you are, the more people will see you, get to know you, and learn to trust you. The more time you spend the more trust you build.
7) Be as polite as possible to any customer - showing patience and kindness will win you repeat customers.
That's about all I have at the moment.
I made my "in" on Sythe through selling rare RSNs. It was very hard to get people to buy from me at first with no posts or vouches, but I slowly built them up and have ~30 vouches.