I did that a little while back. Was instantly approved for AmEx Delta, and then immediately applied for and was approved for green charge card.
Same day apps. Have you looked at PRG instead of Green?? Good luck!!
6-23 app for BCP, approved 2,000.
First AmEx account and "Real cc.
7-4 app for PRG approved.
I think its easier to get a charge card since your paying it every month. I thought id get denied until AmEx saw some history with BCP. Im happy and not applying for anything for a while. Got to age some inquires off my report and get some chase cards. 😀