When climbing people slide back on their saddle so that they can get more of their glutes and quads into the action. Sliding back will help, but it probably drops his cadence.

I agree that the bike is probably too small.

If your knee is in front of the pedal axle then you can slide your saddle back.

The other variable that you have to play with is you crank length. If your knee is in front of the pedal axle then taking into account your leg lenth you can probably get away with longer cranks.

Good luck.