Marble hearth and back panel installed on wooden subfloor

if its a 1930s house I assume its got a chimney breast and the original fireplace has been blocked up and removed. If you roll the carpet back you should find a solid hearth base where the original hearth once stood on. this should be more than adequate for your new fireplace even if the new hearth is slightly bigger. If that's not the case and it is all timber floor then as long as the floor appears solid and free from any rot then that too should be ok

Whenever installing a hearth it is best lay it on a bed of sand and cement. Most hearths are boxed and lipped which means that they are hollow between the top slab and the risers. Also hearths need to be level side top side and back to front. A bed of cement will give you a level base and it will also fill the voids on the underside of the top plinth. Do not use a wet mix as it will draw through the marble and cause staining. Where the hearth meets the chamber there should be a concrete bed placed from the back side of the hearth and into the chamber. This will stop the fire pulling from the from any voids within the hearth area it will also give a level place for the fire to sit