What 3.3volt regulator.
You need a very low drop regulator to power a 3.3volt device with a 3.7volt battery.
An LM1117 would not be suitable.
Do you have enough capacitance on the VCC line.
Do you have all the required pins to ground or VCC (with resistors).
I think enable, reset, and GPIO_0 have to connect to VCC, and GPIO_5 to ground.
https://tttapa.github.io/ESP8266/Chap01%20-%20ESP8266.html
Leo..