I do repairs like this regularly. The process is something called "burn-in." A heated knife melts a solid resin (similar to a finish without the solvents). The hole is filled, leveled, grained, sheen and color adjusted. Unless there are unusual color issues, it should take less than an hour. It's a skilled process to get it right and nearly $100 to buy a starter kit. So it's not a DIY job.

There are people who might charge you "hundreds of dollars" for this repair. I would charge considerably less.