Help! Moldy soil.

Backstory: This plant was dying and the owners moved away and left it behind so I’m trying to give it a second chance at life. I chopped off all the dead branches and propagated what I could and it’s doing okay besides the fact that the soil keeps sprouting mold.
I read that this could be due to remnants of decaying plant matter but I’m not sure how to get it all out without having to fully repot the plant. I’m worried that the plant won’t survive a repot with the cold weather starting. I’m fairly new to plants so any advice is very appreciated.
I’ve included two close up pics of the mold in the soil and a picture of the plant.