I did not check it long time but without apps was possible to make a permiso just using webpage. There was possibility to make it with DNI or passport or precaria.
Also old time trick is just using the passport number wherever is needed DNI.
If you have not enough numbers to look like DNI -add zeros first, if you have too much numbers skip the first ones, assuming it is usually the passport serie and personal numbers are the last ones ( no idea if it's correct for US passport, may depend). it worked fine for me on million ocasions in Argentina, yes it is not 100% correct, but most documents issued here are having some sort of error or mistype anyway.
So get just any permiso with your name on it.