I understand that many stores build their own forums and user communities, and I'm wondering if this is a way to boost sales quickly. Can building a community improve website SEO?
It depends on what your definition of quickly is. Yes, building a community can increase website SEO in many ways, directly and indirectly. Mainly it can help you build a Brand and receive returning visitors directly, which establishes authority and trust and are ranking factors. Think about if you want to go to FB, do you do a google search for Facebook or type it in directly? You can create communities through a Youtube channel, FB Groups, etc. I would avoid forums as they're very difficult to get established with activity.