This paper studies how firms and immigrants’ climbing of the firm ladder shape labor market assimilation. We do so in the context of a historical mass migration shock: the arrival of nearly one million former Soviet Union Jews to Israel during the 1990s. This setting presents several advantages when studying the role of firms and job mobility in immigrants’ assimilation: the nature and numerosity of the migration wave, the fact that Israel granted these immigrants citizenship on arrival, and the availability of population employer-employee data featuring precise information on immigrants’ place of birth and date of arrival to Israel. Over the course of twenty-five years since arrival, immigrants gradually enter higher-paying, larger, older, and less segregated firms. The dynamics of differential sorting into higher-paying firms explain a significant fraction of immigrants' labor market assimilation. E.g., firm-specific pay premiums account for 22-30% of the immigrant-native gap during the first ten years since arrival. These immigrants, who were disproportionately mobile compared to natives, eventually overcome natives in terms of employers' pay premiums, size, and age. The channels we uncover represent an interpretation of wage gaps as (partly) driven by search frictions and firm choices in imperfectly competitive labor markets, as opposed to purely explained by worker abilities.