What creative strategies can a fashion e-commerce site use to acquire customers?

Add a human-social angle to it (but this must be genuine). You can support many not-for-profit organizations, or for every clothing item you sell, you will donate a t-shirt to someone who desperate needs it, or food. People are very conscious of how they spend their money.

If the money I spend on your store has an added benefit versus others, where no such benefit is available, then why not! I'ld rather give my hard earned money to your shop.

Social entrepreneurship can be another way of looking at it. Rather than 'giving' someone a fish to eat, why not train them on how to fish and feed for themselves for the rest of their lives.

Whilst this may seem as an unnecessary burden for many entrepreneurs, but believe me, try it. You will feel good about yourself, word of mouth traffic will come also. By partnering up and/or doing more social / eco-friendly work, you increase traffic as more and more people seem to look for vendors who are more conscious about the world they live in than the buck they are making.