Note that you need some information before you can use your 'blank' vax card. Specifically you need the manufacturer name as well as the lot #. You probably ought not just write some crap there. You would be best served to find somebody you know and trust who WAS vaxxed and essentially use their information.
They say they aren't tracking people who were vaxxed at a state or federal level. If you are going to forge your vaxx record, hope that is true, otherwise you may find yourself on the wrong end of what is starting to look more and more like a totalitarian regime.