That is as far as you can go with him. There isn't a way to get in the private club. If you intend to romance him, you need to call him out on his cocky persona at some point, which can be done the first time you meet him. But if you only want to be fuck buddies, hooking up at the club then telling him you want to keep hooking up will be the best path forward.
There is a little more Alex content I intended to add but cut for time. I may still add it back in, though. His old model was very hard to work with, but his new one will make creating new art for him easier. But even beyond that, this early on he's going to be caught up in work/school a lot. You'll get opportunities to spend more time together/keep hooking up in an upcoming story update.