Then there is the possibility you could fry static sensitive components like the RAM and CPU if you touch their gold connectors (which you shouldn't do regardless of precautions)
You can still build without it safely, but requires some extra thought.
Install the PSU into the case and plug it into the wall (if it has a switch turn it off). That way the case is grounded. Periodically touch any metal bit of the case to ground yourself and disperse any static that may have built up on you.
An anti static wristband is essentially just a wire that connects you to the case, eliminating the need to touch it constantly.
As well as normal anti-static measures such as not standing on carpet and to do the build on a non-conductive surface (A wooden table or stone bench is good).