First off do yourself a favor and adopt some standard schematic drawing conventions with positive power rails always facing up and ground rails facing down, as it is, the schematic is a pain to read.
Most important comment on this thread.
Schematic comments:
For your 5V to 3.3V regulator, please put the symbol vertical. It's really hard to read when it's improperly oriented.
Avoid 4 terminal connections and crossing over schematic traces when possible. It's really easy to have something connected improperly in both scenarios.
I usually add a 100nF decoupling capacitor also to take care of the high frequency noise. Place the lower value capacitors closer to the component than the higher values.
I usually have voltage nets pointing upwards and ground nets pointing downwards.
You don't have any decoupling capacitors for the SIM808. My general rule of thumb is for every VCC add a decoupling capacitor (100nF). Keep this as close to the pin as possible on layout.
Avoid overlapping text or symbols (see lipo connector).
You don't need to create your symbols to follow the connector pinout--I usually place my VCC top and GND bottom. This allows me to orient the nets easier.
No reset button on the ESP32?
I personally would've kept all the ESP32 components directly connected on the schematic.
Layout comments:
I prefer 4 layers for prototype boards (signal, gnd, power, signal). My preference and it's pretty cheap usually.
You can use polygon pours.
A lot of people prefer not to use 90 degree angles.
I'm sure you could get rid of a lot of your vias.
I can't tell where the ESP32 chip is, but if you're using the SMD chip make sure the antenna is not on the board/near anything that could have interference issues.
Some of your traces look strange--in the future I would suggest sending each layer. I can't really understand it as of now.
Try and keep capacitor values (especially decoupling or clock capacitors) as close as possible to the pins.
Just my 0.02. Take everything I say with a grain of salt.