Attempting GFCI with limited wires, need help

So I have a light and a switch in my bathroom. The goal is to have a lightswitch/outlet/GFCI combo in the light switch box controlling the light with the outlet constantly having power regardless of switch position.

I have 2 electrical boxes in the bathroom:

One box with the light switch/outlet combo (the outlet half never worked) with 2 wires coming in, a black and white wires to the switch half that controls the bathroom light.

The other box has the light mounted on it, has 4 wires coming into it, from the top of the box a black and a white (assume hot and neutral), and a black and white going to the switch box for the light switch.

Originally the light switch controlled the bathroom light and had a dead outlet that never worked in it. Is it possible to get the light switch working and outlet to constantly be powered (I bought a GFCI combo) WITHOUT running additional wires?

Ive included pictures of everything. Thanks!