Your house must be built on a slab. That means you have a down flow furnace. If the installer did not include a filter that is surprising. It is not a difficult job to install one in the air return at the furnace. I would make sure you are correct about the "down flow".
I would call a pro. It should not cost too much to have them install one. Now is the time to think about maybe installing noe of the better filters. Some of the new electro-static filters work pretty good and don't cost a kings ransom.