hi Andrew and welcome, No, its not impossible to lay slabs without mixing concrete, you could just lay them on a bed of sand but they will never be either firm or secure and you will always have a problem with weeds growing up through them ! Even it you first put a layer of weed fabric under the slabs, that wont stop weeds in the cracks !! Slabs on thier flat are not the best things to erect a greenhouse on, they are fine for the floor of the greenhouse but i would advise you either lay 2 rows of bricks or ideally a row of 4" concrete blocks (laid on thier edge) on which the frame will sit ! This will have 2 main advantages, firstly it gives you much more headroom and secondly the weight of the concreted in blocks will anchor the greenhouse in the event of a gale (which the slabs wont do)
The easiest way to put the base in is to scratch out a shallow foundation (the size of the greenhouse) lay the blocks on a shallow bed of concrete, you only really need enough under them to level them as the strength is when the blocks are pointed in ? make sure the base is square, do this by getting the diagonal measurements the same length, put the greenhouse on the base and them you can point the blocks in. If the base is not square, you might find the roof glass wont fit ?? doing it this way, its not then so important to lay the slabs on concrete, sand will then be fine !
Hope this helps, Lannerman