I want to get residence permit and stay at this country. We plan to get to Argentina as a tourist, then register monotributo and sign a contract with local employer. Is it real way to reach the goal?
Probably, the "easiest" way for you to get a DNI in Argentina is to get a "student visa" which will get you a DNI and a CUIT/CUIL (taxpayer identification number).
To get temporary residency based on being a student you must enroll in an institution that is approved by migraciones.
If you don't speak Spanish that might be difficult..It is something others may be able to clarify.
There have been jokes recently about getting a "fake enrollment" but in the case being joked about, the enrollment was real.
It is the student that is "fake" (in the sense that he has no desire to be a real student and enrolled just to get the visa and the DNI).
After you get the student visa you will receive the DNI with the CUIL/CUIT.
Then you can become a monotribusto and work for yourself or (as far as I know) work for someone else without prior approval from migraciones.
In order to be able to renew the student visa after the first year, you will actually have to have completed the required course of study.
Migraciones will check to see that you have done so.If you have not, there will be no renewal.
The temporary residency conveyed by the student visa can never be "upgraded" to permanent resdiency, but you can apply for citizenship while you are here with a student visa.