while not preferable of course, it is possible to stand on carpet and assemble a computer without an esd wristband. just standing on carpet doesnt mean all of a sudden you will get a static discharge.
as long as you are not shuffling your feet around and generating a charge and as long as you make sure to touch the pc case often before you touch any components you should be fine.
i've never used an esd strap, even for my first builds. its a good idea if you dont know what you are doing however if you touch the case before you touch anything else each and every time you will be fine.
standing on a plastic office chair mat or other such surface (or sitting in a chair if you prefer that) would also work and would reduce the chance that you build up a charge.
i shouldnt have to say it but make sure you do not wear a sweater, sweatpants or other clothing which generates a static charge.
generally i install the power supply into the case first, then the motherboard. i then install everything else such as the ram once i have the mobo mounted. some cpu coolers however might require mounting before installation if your case doesnt have a hole behind the motherboard tray.