N-channel MOSFET used to control 5V relay from 3.3V ESP8266 pin
I found the following schematic on this website. Its likely incorrect in some parts though, as S8550 is a PNP part, they probably meant S8050.



Since you stated that directly plugging a 3.3V signal didn't work, you can try one of the following (considering your N-FET limitation):


Use your IRLZ44 to directly drive the relay
Put a resistor in parallel with R3, to increase the current going into the NPNs base and try to trigger it with 3.3V again.


p.s.: I hope you aren't actually connecting GND to AC with your relay as it could be quite unpleasant/dangerous: