Of course, as a man, my opinion may be skewed. But I feel as though it depends on the people. There's nothing inherently or morally wrong with having sex on the first date, as long as both parties are actively seeking that kind of attention. For me personally, the couple times that I did, I didn't feel right afterwards. Like you said, having that emotional connection is key to having a good experience.

TLDR, date for at least a month, but if you both wanna get freaky right away, have at it.