My guess was that
Squark ⚧❤ started early summer and has just found the lake encounter without school starting. I don't know if it is supposed to be able to be triggered that early, but it can be accessed from day 1 I think.
My understanding is that you need to have a higher friendship rating with her before you can actually get the real home invite. I kind of felt it to be like the way someone would say "we must meet up soon" but with no intention of actually following up on that. Being friendly with her at school and the disco should get you a real invite... though you may need to go with her after school at least once to find the house, I am unsure.
You can go to her house without getting real access to it during the fall, when walking her home if she likes you she invites you in. and after the fall she will take you to her home for a hook-up, but neither of these events give access to choose to go to her home outside these specific events, though the post fall hook-up can be repeated whenever she is at the disco.
As it stands, if you get the real invite before the fall, you can choose to go to her home (during social hours) and get invited in, have a look around, and interact with her. But once she has fallen you will not get past the front door, her mom will never let you in. (But as I said above, you can still do the post fall disco hook-up.)