How can the charge time/startup time for a boost generator be calculated?
If you assume that there is no fancy start-up control algorithm to prevent potential output overshoot or diminish inrush currents, then you can model the boost converter as operating in DCM (load is light hence DCM is valid) and, for each switching cycle, a constant energy is transferred to the capacitor (based on a fixed duty cycle). Use this formula to calculate the new voltage for each dose of energy per switching cycle: -
$$\text{Energy} = \dfrac{1}{2}\cdot C\cdot V^2$$
Of course after the first energy transfer event, the capacitor starts to acquire terminal voltage (call it \$V_i\$) and the next energy transfer lifts if from \$V_i\$ to a level a little bit higher. But each subsequent dose produces a slightly less increase in voltage as per the energy equation of a capacitor being related to voltage squared.