Can the AI assistant build a website like one I already like?

Yes. Give the AI assistant a screenshot or the URL of a website or landing page you like and tell it to build one like it, with the changes you want. A design from a different niche works well as inspiration to adapt for your business.

You can also find design ideas on sites such as Dribbble and Behance and feed those examples to the AI. AI learns best from examples, so showing it pictures of what you like works better than only describing it.