As far as what you can do you have a number of options. Definitley get a filter before you even start it. The last thing you need is to suck a leaf or small bird into your engine.
1, get some money back on your purchase cause I would feel ripped off if I bought a car without a filter on it. Id also feel very uneasy about it.
2, take it to a shop and tell them you bought the car, discovered there was no filter, and that you want them to check it out and make sure its ok. I dunno what they will do, maybe check compression and pull the intakes to see any signs of dirt buildup on valves.
3, change the oil and put in some additive that A&A sells. Its in a silver can and its supposed to restore lost compression. I forgot the name.
Bout all you can do. It will be ok as long as it didnt suck too much dust and **** into the cylinders. That will mess any car up.