I am a retired lifelong carpenter/ building Contractor. I also ran my own line in my house after it was built. As @winoguy17 says, You can go through the crawlspace (if you have one) If Not then go through the the attic. There will be no need to cut Sheetrock except the hole for the remodel box. If you have a 2 story house and trying to put this on the 1st floor in a home without a crawlspace, it can still be done without much cutting of Sheetrock. This will take a lot of measurements and planning and is not for the typical DIYer.
Depending on where you live and how strict the codes are, an electrician should be able to do this for maybe $750-$1k. The later situation I spoke of will be more $$$, maybe double that price. One caveat is that this cannot be done in exterior walls due to the insulation without removing Sheetrock. Of course , the price then increases to double or more. Again, its all dependent on where you live and the bureaucracy & codes. Also some city codes are very cumbersome and this too raises the price.
Also, I agree with @helmholtzsoul concerning the 12g wiring. Most outlets will not accept 10 g and you would have to junction it over to 12 g anyway. Good luck