I will help you communicate why your product exists and how it can make your customer's life better. This is the fundamental communication problem for new businesses, and it's the problem I built my company Outbound to solve (now as part of Zendesk).
It depends whether this is your first market or not. Going live with limited supply is usually inevitable when it's your initial marketplace launch. In this case, you should look for a differentiating benefit that you can control and deliver to your demand side customers regardless of how quickly your supply ramps up.
For example, when Lyft launched, there weren't many drivers (supply) so a taxi might be faster, but if you waited they would drive you wherever you wanted, even out of the city, whereas a cab usually wouldn't. Getaround offered lower than Zipcar prices in exchange for sparse supply and longer wait-times to get car owners to approve your rental request.
But if you have already launched in one market, I would focus on that before launching another. If you figure out those dynamics first, you will waste less time and money in the new market.