Is it possible to use just a capacitor to debounce a button?
It depends on what the default state of the switch is. A capacitor will only charge when you give it a positive voltage. Usually, in an embedded environment, we use a pull-up to give a pin a default high state, and link the switch to ground. Adding a capacitor won't help here, because it won't "store" the ground state.

However, you can also use a pull-down. This would mean the pin is by default low. Making it high by pressing the switch, will charge the capacitor. After releasing, the capacitor will keep the pin high for a little while, so yes, this would work. I'm not sure if 1uF is enough, too little or too much, I'd recommend you to look with a scope and try it out a bit.