Yes, there are many examples of businesses that have launched their website and taken orders before placing a big inventory order. This approach is commonly known as dropshipping, where the business acts as an intermediary between the customer and the supplier. 

One well-known example is the online marketplace Shopify. They allow businesses to create their own online stores and start selling products without having to invest in inventory upfront. When a customer places an order, the business simply forwards the order details to the supplier, who then ships the product directly to the customer. Shopify provides integrations with various dropshipping suppliers, making it easy for businesses to start selling products without holding inventory.

Another example is the company MVMT, a popular watch brand. When they first started, they used a dropshipping model to fulfill orders. They created a website, showcased their products, and accepted orders. Once an order was placed, they would forward the order details to their supplier, who would then ship the product to the customer. This allowed MVMT to validate their business idea and generate revenue without investing in inventory upfront.

Dropshipping has become a popular business model, especially for entrepreneurs who want to start an online store with minimal risk and investment. It allows businesses to test the market demand for their products before committing to large inventory orders. By launching the website and taking orders first, businesses can validate their business idea, generate revenue, and gather customer feedback to refine their product offerings.

References:
- Shopify: https://www.shopify.com/
- MVMT: https://www.mvmt.com/