Toddler climbing out of playpen

My son just turned 1 and unfortunately is a climber. He climbs out of his playpen. It can be pitch black and he will still get out and walk around.

We tried to put him in a toddler bed but he won’t stay in it. Last night he didn’t go to bed until 2 am because he was constantly getting out of bed. Then, he was up at 6am. There’s absolutely no way to keep him in it. We live in a tiny apartment and have no where to put him where he would be confined. Like a room and shut the door.

He’s not sleeping at night because of it and won’t take a nap either because he’s too excited knowing he can get out. I don’t know what else to do