What is the best way to grow a 2 sided marketplace apart from paid advertising?

Hyper-localised guerrilla marketing can work at the beginning. At JOB TODAY, we stencilled the floor in a few locations, tying our value prop into a public holiday to generate signups on the jobseeker side of our platform. To sign up employers we focussed on phoning employers who were using rival platforms 👻

You should identify your "hard side" of the marketplace and start working with it. Once you have a critical mass here, start bringing customers over from the other side. But you need to create some value for the hard side in a "single-player" mode - i.e. when they are the only side of the marketplace.
For example, when OpenTable wanted to create value for restaurants, they provided free software so that restaurants could manage bookings, which attracted restaurants onto their platform before they opened up their platform for customers. Then they proposed to bring customers to restaurants in exchange for a commission. It was a no-brainer for the restaurants because they were already using the software; it was useful for customers because there were a lot of restaurants listed on the site when they opened it up for them.

In the WBE Space we were actually doing something similar. My advice is to start in a very small niche where you can reach both sides of the market and convince them to join. You can create a community for example or a facebook group, and only once it's big enough announce the website.
Another idea is to build a product in such a way that just by creating a profile the users will be getting some value (maybe they have a way to organize their ideas, or showcase their profile)

I believe this is where you use the Uber model of chicken and egg to achieve product market fit.