Look for inspiration in the boxes you might have in your pantry, or from toys or small appliances or gifts you've received. Something with a clear plastic window is fun. You can spray paint the box.
We had a large thin square box that had a clear front. We made it look like a little computer monitor. We used the lid of a shoebox for the "keyboard," (the keys spelled H A P P Y V A L E N T I N E S D A Y !) and then a tiny box with a long pink heart cutout glued to the top for a computer "mouse." We spray painted some parts silver, and attached it all together. There was some writing on another cutout that said "Download Valentines here" with an arrow pointing to the opening. Sounds complex but it was just something we kept adding to as we saw it come together. Can't throw it away now!
They probably want it to open so that bigger items can be dropped in and/or so that the kids can easily look at their valentines. So maybe it doesn't necessarily have to have a removable lid, but just a large flap.
Now I'm visualizing an idea that has a little shoe box standing on its end. There could be a large cutout of a cute bear or mouse, attached to the bottom of the shoebox and then its arms wrap around the box right over the lid. So the overall effect is that the animal is holding or hugging the tall box. Maybe a bit of velcro so the arms can let the box be opened.
Good luck! I'm sure your daughter will end up with a cute box. It's nice the preschool gave you advance warning!