Now I want to know, how to add larger than 10uF cap?

Why? 10uF is already pretty beastly, and the point is to dampen signal verses intermittent drops and drains, not power the backing device for any amount of time.

You need a soft-start circuit between the USB connector and your big cap. When you first connect the USB device, the cap has no charge (0V) so it appears as a short to ground to the host 5V supply. The result is a large current spike which can draw down the host supply below some functional threshold or even damage it. We could oversize the host supply to deal with a 25 A transient and add cost and introduce safety concerns or push the solution to the connecting device where the problem exists. The solution is to ramp the current up "slowly" over several ms using a transistor on the device side. While the transistor is turned on slowly, it isn't fully conducting, acting as a variable resistor. The transistor is dissipating power during this transition so it must be sized correctly and timing controlled deliberately. Hence why we want the same design to contain the cap, transistor, and ramp control. A typical circuit might be: connector->small cap->soft start->big cap->main circuit. The soft start feature is often just built into a voltage regulator since there's already a transistor and control circuitry there but you can also get a dedicated load switch if you only want ~5V. The 10uF requirement is a contractual agreement between host and device that ensures compatibility between devices. If you don't follow it, a sophisticated host may simply cut power when it sees the current spike and that would be the device's problem.

Realistically, most USB devices hiccup when they exceed their current limit, especially in 5V mode. And since caps don’t loose charge that quickly typically, you can usually charge the cap up enough to deal with this transient no matter how big your cap is (unless it’s something absolutely enormous… which wouldn’t be implemented for cost reasons)

I have seen this play out with host devices with robust current limiting outputs. Sometimes it works for the connected device and sometimes the device sabotages itself when its own regulator turns on at say 3.6 V, drawing down the partially charged input cap below the regulator's UVLO and turning itself off again. Then the cap starts charging again and the cycle starts over. Depending on the host implementation, the burp mode may not reset without a full disconnection, at best leaving the connected device to sip a low average voltage and low current or persist in the above loop forever. Making sure this doesn't happen is more difficult than just implementing inrush limiting.