A capacitor like
C3 will only filter and smooth the voltage; it won’t boost a 3.7V input to 5V by itself. If you're aiming to get a 5V output from a 3.7V battery input via
J3, you need a boost converter stage (for example, using the
U5) configured correctly. The capacitor would then serve as an output filter at the boost converter’s 5V output, not as the conversion element.