This can be hard, to do but I've got a trick where I copy the PS2 game on to a DVD-R and play it from that.
If your PS2 Slim can't be softmodded like mine, you can look up online how to unblock all the things that stop the disc from spinning, then back up your game, then put it on a DVD-R.
Once this is done, grab the original, start it up, find a good spot where nothing is happening (Such as in a movie, or a menu screen), then swap the discs.
Be careful because you can mess up the disc.
Also this can't be used on games with internet access (Such as Football), because sometimes it goes to a special file type the triggers the PS2 to check if its an official disc (unless you have an old model).
(If this is bannable please tell me, because I will gladly clear this post)