This is an extremely common problem. If you are using PLA you shouldn't need a heated bed to keep it sticking but a heated bed is one (expensive compared to others) solution.
My favorite solution is to use blue painters tape on the bed and to wipe the tape with isopropyl alcohol (aka rubbing alcohol - found at any drug store). In fact you may have a new problem - removing parts from the bed
Also you could round the corners of your box. Or add a single layer of material beyond the edge of your box with a large round radius on each corner. Or you can use the Cura option to print a "raft".
If you have pointy cornered box, all the lifting force is strongest at one tiny point at the corner of the box - once that lifts, it keeps going. However if you have rounded corners the force is distributed across the curve of the corner.
But again, you shouldn't have to do any of this if you use blue painters tape (came with ultimaker - available wherever you buy house paint) and clean it with isopropyl alcohol. I think the alcohol removes the glue residue from the layer above when the tape was still in the role.
There are various threads here discussing warping to give you more clues but generally the HBP will help and /or printing first layer very close to the platform and adding 20mm pads .2mm high or similar to corners of your model.
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