This should unlock near the end of Chapter 1. I can confirm you can use replay chapter Explore mode to grab items you missed.
Chapter 1 - Plush Toy - Found at the start of the game, look at the big bowling mascot than take a small one next to it.
Chapter 1 - Arcadia Photos - When cleaning your place start with the memories box which will leave behind a few photos. Pick them up and head upstairs to put them on the photo wall.
Chapter 1 - Abraxas Box - When arriving at school for the first time walk forward and a scene will play with Reggie throwing a box on the ground. Pick up the box and solve the first layer with Reggie.
Chapter 1 - Origami Note - Still outside the school go to the big statue outside the FAB. On one of the benches is a pink origami to interact with. Open it up twice to collect it.
Chapter 1 - Abraxas Rose - Near the end when needing to comfort Moses in the FAB. Check the table outside the offices for the rose.