Probably not 'max' speeds, no.
IF you're far enough away (or with enough obstructions) to not pick up Wifi, and cannot run ethernet...... and your home is (relatively) new, Powerline would be a solid option.
You can configure a lot of old routers (maybe you have one laying around?) to be a repeater. The problem there is it's still Wifi based (and in your case wifi in, ethernet out). Still potential for added latency and, depending on how far from your main router you need to place it to be able to run an ethernet cable, it may have to deal with the distance/obstruction issue you're dealing with for wifi.
**EDIT** Actually, your post isn't too clear as to whether you simply cannot get ethernet, or also cannot get Wifi in your...