It only shows up/gets reported to credit agencies when the first statement cuts.

Most issuers consider approval date as the date account was opened. So if it was instant approval, you know the date. Also if it was approved with recon over the phone, that's the date. Where it gets tricky is if you didn't get instant but you were approved by their review processes. In that case, you may need to call or send a Secure Message to find out when you were actually approved.