Get a quick win
In psychology, there is a cognitive bias called the Halo effect which is "the tendency for positive impressions of a person, company, brand, or product in one area to positively influence one's opinion or feelings in other areas."
In the show 30 Rock, there is a hilarious episode featuring the good looking Jon Hamm who lives in a "bubble" where everyone treats him great because of his attractiveness. He is actually terrible at everything, but because he is good looking he can get away with it.
You can take advantage of this cognitive bias by getting a quick win with any project you start.
For example, I half automated some data cleaning and analysis that the client was taking weeks to do and shortened it to an hour. I did that within a few weeks of starting and the client loved me for the rest of the project. It also gave me enough street cred that the client accepted my submission for a new employee despite not formally meeting all the qualifications.
If you are trying to get your first 1099 gig and you're starting a new project or getting a new client, try to get a quick win. This can help you eventually convert your job into a 1099 role and/or turn your client into a valuable member of your professional network.
If you are starting a new 1099 gig, getting that quick win will help you solidify your reputation as a top performer and give you opportunities down the line. Plus the prime will never want to lose you, giving you leverage.
OR, you can just be really really incredibly good looking. That is also a valid strategy.