You can try some adhesive like liquid nails or PL200. If you can lay the sheet of OSB flat, glue 2x4 or 2x6 to the sheet, then you can come back the next day and screw it together.
I do not understand what the purpose of the bed is. Is it to keep dirt and water from getting on the floors or is there some other reason.
I would line it with plastic. OSB sucks up water like a sponge.