Yes you do need an incubator. Bacteria aren't a simple chemical reaction that just runs more slowly at room temperature. Many bacteria that live in your mouth will not grow at all at room temperature.
I'm not saying someone couldn't hack together this experiment. I'm saying a middle-schooler who can walk into a lab and prepare everything in an afternoon under professional supervision is at an advantage compared to a middle-schooler who has to gather all this equipment and knowledge over the course of weeks and months (which will still be inferior from a non-didactic point of view) without the support of their parents when it comes to performing a valid scientific experiment.
I'm not saying someone couldn't hack together this experiment. I'm saying a middle-schooler who can walk into a lab and prepare everything in an afternoon under professional supervision is at an advantage compared to a middle-schooler who has to gather all this equipment and knowledge over the course of weeks and months (which will still be inferior from a non-didactic point of view) without the support of their parents when it comes to performing a valid scientific experiment.