You should not do it simultaneously. If you do you will waste a lot of precious resources.

The general rule is that you should start with a supply in your case with the list of experts. The best practice here is to start with experts in some niche field (for instance not finance experts but rather financial controllers that help startups in pre-seed stage) and also in a specific area (city or even neighbourhood).

To attract the supply side there are a couple of proven strategies:
- Job offers. You advertise this as a part-time job on job sites and leverage the traffic from job sites to yours. Its a fairly cheap way.
- Calculators. You build salary/gig calculators that help supply side to calculate how much can they earn/or how much should they earn and convert them on your website.
- Create the content on the niche subject and post it like a mad person on relevant groups in FB, Linkedin, Twitter etc.
- Scrape your competitor's websites for contact data to your supply. Airbnb did this with Craiglist.
- Create referrals for your supply to invite more supply. Uber did this at the beginning of their operations.

Once you have a couple of them you can start offering their services to a niche customer (demand side).

Once there is enough demand you refocus on supply again to either add more experts in the same niche or add another niche.

Marketplaces are like production lines you always need to focus on bottlenecks, once you figure out one you need to move to the next one.

There are however strategies when companies start with the demand. Its called it "Fake it until you make it". Nobody speaks about it however the majority of startups use it. Basically, you set up fake profiles and advertise it to the demand side of the marketplace. Once there is a request you start looking for supply.

Oh and you don't need code for this. Designer, Google sheets, zapier, typeform or Wordpress (Airbnb started on Wordpress). You should not spend more than 200 $/month for a subscription to these tools. You can use also platforms like Sharetribe that have all the basic marketplace functions built in.

Good luck!