If you don't have another creature you can activate: No, you can't do that. You can only quickcast before or after any friendly creature's action phase. In this situation, you don't have a friendly creature's action phase to quickcast before (and there's no retrocausality or anything - think about if your Rouse the Beast was negated!). You'd have to wait until your final quickcast phase, but that would be worthless, since you'd never get a chance to activate the creature.

If you do have another creature you can activate: It seems ambiguous whether you can do this or not. Having just reread the relevant rules, I'm inclined to say yes. The rules make it sound like you choose the creature just at the moment that you flip the action marker. So while it's implied that you're taking some creature's action, which creature is not determined until after the quickcast. Since your creature will be ready to activate after the quickcast, you can choose it. But again, this is just my opinion.