From what I understand, unlike in Cuba or Colombia or Mexico, most predominantly-European citizens of Argentina are descended from 19th and 20th century immigrants rather than earlier Spanish colonists. And unlike other colonial immigration destinations like the United States, the profound majority of Argentina's immigrants were from Italy.
What effect did this have on the preexisting language and cultural traditions of Argentina? Did Argentina's governments during these period forcibly assimilate these people?
Argentinian history teacher here!
To start off, you must understand that, unlike for example Mexico, Argentina was mostly a frontier region during colonial times, extremely underpopulated and with a relatively (by colonial terms) egalitarian society. By the second half of the 19th century, when economic growth accelerated and inmigration grew exponentially, Argentina's social structure was in flux. A local landholding elite had consolidated, but few of them could realistically claim long heritages and their attempts to "close themselves off" to the newcomers were mostly unsuccessful. To this day, a large section of the economic and social elites of our country are direct descendants from these late 19th, early 20th century italian inmigrants (the current presidential family being a prime example).
So, at the top you have a somewhat open elite that lacked the means to effectively exclude the newcomers. But what about society at large? Well, the argentinian state went about nation building, of course! The assimilation of the large italian inmigrant population was carried out in several ways. First and foremost, in 1884 Congress approved Law n° 1420, the first comprehensive legislation regarding primary education. It took primary education away from local goverments and the Church and put the national goverment directly in charge of providing compulsory, free and secular education. The public education system grew rapidly and for the most part meant that the sons and daughters of inmigrant were quickly integrated into the nascent argentinian national identity promoted by the state. A law approved in 1901 establishing compulsory military service played a similar role. The assimilation process was facilitated by several factors: unlike say the United States, inmigrants found a preexisting society that shared certain characteristics with their own; first and foremost, religion was not an issue, as Catholicism was a shared religion by both "natives" and inmigrants. Spanish and Italian were and still are relatively similar, and made for an easy transition for the newcomers (unlike English).
The effects of italian inmigration where vast. To this day argentinian spanish (also known as rioplatense spanish) shares many loanwords and phonetic similarities with italian. Argentine diet is to this day heavily influenced by italian cuisine. Italian inmigrants were also involved from the start in the development of several key aspects of current argentinian popular culture, like music (where tarantela and other traditional italian musical styles were heavily influential), football (soccer for our american friends), etc.
Hope this helps! Cheers!