Do you really need to "build culture?" How about "do an honest job for honest pay and live your life outside work on your own"?<p>"Build culture" sounds a lot like "lure people into working more for less compensation" anymore. With such limited interactions available, you just have to be your own culture.
You could write some pages on your website, about how you want the culture to be, what's important to you and what cultural things will make the company great. Then try to live all those things
It always starts with screening people on the enter (who shares same values and culture).<p>Some successful remote companies i know do regularly few days offline meetups, team buildings etc.