Is it possible to create an experiment in house conditions to prove the existence of germs?
You could use Jell-O for growing bacteria if you don't have access to agar ! (I have never tried this but I think it should be possible because the gelatin in Jell-O is like agar.)

You should first sterilize a small knife on a gas stove or with alcohol and then gently rub it on any surface (where you think bacteria are likely to be found ) and then rub it on Jell-O taken in a dish. You should then place it in an environment similar to the one from where you isolated the bacteria. After one or 2 days the bacteria should grow. 

For control : You could simply put a plate of Jell-O in the same place but without inoculation of bacteria.

Disclaimer : I am not a microbiologist and I am not sure this would work but you could give it a try as it will not be really expensive :)