When we arrived in America my mother's first job was at a deli. There, she did not work for Russian speakers, if I recall correctly, her boss was from India. She quickly began to learn English, because she needed to know the different varieties of fruit, vegetables, and cuts of meat. And how to cut, because she cut and sold everything there. Her boss did not speak very clear English, it was New York, so the customers didn't speak clear English either, so thanks to the variety of accents and the volume of food, which she had to constantly explain, she quickly began to master the language. So I'd say the assimilation process, especially in New York, went pretty fast.
Then, she went to NYU and worked for a real estate agency. With every new job, the American dream came closer. After almost 10 years, we moved to California. By that time, everyone had already assimilated to America. The rest is history.