The main problem with running cables under a carpet is damaged to the cables. People will step on the spot and the cables can get damaged over time. It is best to put the cable under both the carpet and the padding. If you just put the cable under the carpet there will be a bump where a crease can form. You can try a fish tape but fiberglass rods are the easiest. They won't bend and get stuck as easily. I was a custom cable installer for more years than I care to mention so I have done it a few times.
The way I did my cables was to run it through the basement. I did a small wall fish about a foot to the basement on each side. Then I ran the cables down through the wall to the basement and up the other wall. But it all depends on what your floors are made of. I have original Victorian hard wood floors that I did not want to damage. If the floor is just plywood then I would not be that concerned.