@salmanirfan my first point of interest would be why it melted. There may be more damage than just the port. Post a couple of well focused and large images of the damage, the board etc. with your Question.
If it is "just" the connector, you could replace it by soldering a new connector in its place. USB -C ports are a bit more involved due to the pins on the underside. You will need a good rework station and experience to replace it. To disassemble it use something like [https://www.youtube.com/watch?v=R-nw_5dyhew|this video] and/or [https://www.youtube.com/watch?v=yXe4AEXSmeI|this one] It might be a slightly different model but it should still work for your Bose as well.
There will be a challenge to find the replacement connector. You may have to find one that fits, by scouring Digikey.com or Mouser.com I would recommend that you replace the complete charging board. You would need something [https://www.joesge.com/products/bose-nc700-noise-cancelling-headphones-700-charger-port-pcb-type-c-parts|like this] Example only.