Well, my uncle crossed the Andes Mountains during last dictatorship government in Chile, there are several paths but it is probably the most dangerous way to do it. Specially because there are mine camps regarding the 3 times we almost have war with Chile.
In Misiones during night you see several boats crossing the border, Uruguay river is not so wide as the Paraná is.
The border with Bolivia is riverless. And it is corrupted, the illegals Chinese cross the border there in bus, they just bribe the border control. But this is no man´s land. Salta is also the cocaine route, so it probably is more dangerous than the mine camps.
But the easies is for sure to cross de la Plata River during a beautiful weekend in spring or summer time where there are thousands of small vessels around. Nobody will notice you.
But...escaping illegally from this country? Come on! There is almost nothing a lawyer cannot solved keeping you out of jail. But if you try to escape, and your are caught, you will pass 4 years waiting for trial in a jail. And perhaps .on trial you will sentence innocent. So, as a criminal lawyer, escaping is the most stupid idea.
Regards