How do I make a two sided marketplace work in the children's fashion and accessories niche?

This is always a chicken and egg problem. You wont attract customers if you don't have sellers on your market place and sellers won't join unless they see numbers.
This is how I would approach(I won't call it optimal as there is nothing like optimal here as strategies will change based on time, place and demand dimensions)
1. Start from a locality or a city with sellers who are known to be providing good service to their existing customers. Go and pitch to those customers on how they will benefit on their supply chain if they choose your market place. Now once they are on-board to your platform, go talk to their customers on how you are making their life simple by coming to their platform.
2. Slowly expand to other localities and make sure that you add varieties to your platform in the process. Choose the sellers who will provide a wide range of goods in the process.
3. Expand this at a city and then go for state, country and cross-country level.

As you build up the model, make sure you respect the credit cycle of buyers and delivery cycle for customers.e are nuances you want to take care at each level.Setup a call and we will go over this in detail.

Having operated an online marketplace for 3.5 years, it's no easy feat. If you would like to setup a call, I can tr to give you as many of these learnings as possible, before you get started.

I ran one of the top accelerators in the US for several years and I'd say 50% or more of the businesses that come through face this problem. I've seen a lot of patterns in this space and I could advise you if you are interested on what has worked for some of the businesses I have seen. The chicken and egg problem can be overcome with the right planning. I'd be happy to schedule a call with you.