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TPS61094: Supercap not being charged due to capacitive load?

Part Number: TPS61094
Other Parts Discussed in Thread: LMR66420

Tool/software:

Hi,

We've got a problem with the TPS61094 in combination with a supercap and a capacitive load.
The TPS61094 is fed by a DC/DC buck converter (LMR66420) at 3.83 Vin.
The output voltage is selected as 3.6 V. 
On the output of the TPS61094 are various things: an LDO linear regulator for an additional voltage rail (which in turn has an MCU and other peripherals) and a modem. 

Upon powering up the board, the supercap does not charge and it seems as if the TPS61094 is just in force bypass mode:
Yellow: VIN, Blue: VOUT, Purple: VCAP

However, when I remove the two large capacitors (alu/poly 180uF each) from the modem, the supercap starts charging upon powerup (can also confirm by looking at the current drawn from the bench PSU):

I cannot toggle the MODE or EN pins on this board, as they are permanently tied to VIN without 0R resistor unfortunately.
We would prefer not to add components if not required, but we were thinking perhaps we need to toggle MODE/EN pins after a short delay, waiting for the output to stabilize first? 

Any help is much appreciated!