Ventured over to leftist space, here's the data they often cite to show that immigration DOESN'T hurt wages much:

https://www.nber.org/papers/w12497.pdf National Bureau of Economic Research paper on the effects immigration has on wages in the United States Study contends previous analyses on the relationship between immigration and wages falsely assumed perfect labor substitutability between immigrants and native workers of similar education levels, distorting results Research shows average American wage RISES due to immigration, both short-term and long-term Only native demographic whose wages drop are High School dropouts who suffer a decrease in wages of approximately ~2% short-term, alleviating to ~1.1% over time. Study finds new immigration does severely impact wages of prior immigrants, suggesting lack of substitutability with *natives. Overall, vast majority of American workers’ wages increase from immigration, High School dropouts (<10% of population) experience a slight decrease which alleviates with time (and there is evidence that immigration may increase native High School graduation rates, too).

https://sci-hub.do/10.1016/j.labeco.2014.05.002 Similar research to the above paper, except conducted on the French labor market. Findings are near-identical; immigration leads to across-the-board wage increases for all except a small minority of low-education native workers. Reaffirms conclusion that there is low substitutability between native workers and immigrant workers.

http://davidcard.berkeley.edu/papers/mariel-impact.pdf Famous research on the Mariel Boatlift and the impact of a wave of Cuban immigrants (mostly low-skilled) on the economy of Miami. Research found essentially no impact on native wages, even for low-skilled workers, despite the Mariel Boatlift increasing Miami’s labor force by seven percent. Even former Cuban immigrants didn’t seem to be affected.