Can ESP32 Power Up Directly Into Deep Sleep?

[skillz43132]

I am planning a project which involves an ESP32 being powered by supercapacitors, which are charged by a small solar panel. The ESP will be deep sleeping mostly, only waking occasionally. I am planning on using an LDO regulator for the 3.3v rail of the ESP, so that I can get the widest voltage range out of my supercaps.

I have some concerns over the following scenario: As the supercaps begin charging up in the morning, and the voltage reaches the threshold voltage for the LDO regulator to become active, the ESP will likely draw a spike of current as it boots up. I think this may cause some issues, as the voltage of the supercaps will likely immediately drop below the threshold of the regulator, causing the ESP to power off again. I'm concerned that this oscillation behaviour may cause the ESP to never properly boot up.

I was wondering whether the ESP is able to start deep sleep directly on boot? This way, the ULP can wake the chip once the supercap voltage has risen to a suitable level, with a slight voltage buffer beyond the LDO regulator's threshold voltage. I can enable deep sleep in the first line of code, but I don't think this will bypass the initial current spike, as the chip still has to properly boot up in order to execute code on the main cores.

I have the option of using some external components to control the RST pin to only allow the ESP to activate above a certain voltage, but that will add complexity, so I'd like to know whether there is a purely software solution to this issue.

In conclusion, is there any way for the ESP32 to directly power up into deep sleep mode, such that the ULP can wake the chip after the supercap voltage has passed a certain level?