How to deal with a complex circuit of resistors and capacitors?
You know (or can assume) that initially the capacitors have no charge => the voltages across each capacitor is 0.

Now remove the capacitors for a moment. Think what the voltage across the lower (ex-) capacitor is. (If you don't see it immediately, calculate the voltage at its right side, repeat for its left side.) repeat for the upper capacitor. Conclusion?

Now calculate the current.