As long as it doesn't affect your attendance at work. American universities attach great importance to your attendance and your performance in class. Don't let part-time jobs affect your study.
About scholarships. There are many kinds of scholarships. You should take a closer look at the school materials. Even if there is no scholarship in the first year, it doesn't matter, because if you do well in your studies, you can still get a scholarship in the second year. What's more, a large part of American universities don't have scholarships for international students in the first year. For example, the University of San Francisco, Washington State University. International students at Washington State University still have a chance to get scholarships in the second and third years, while at the University of San Francisco, international students don't have 1 cent.
For you, the most economical way is not to work, but to study well. Because even if you get a full prize when you are admitted, you will still lose this scholarship if you don't get good grades after studying in the United States. Therefore, you should pay more attention to your studies. Part-time job is only an aid, because no matter how hard you work, as long as you want to graduate from a regular university, the money you can earn may not cover your living expenses.
By the way, if you insist on not going home, you can have a rest in the summer semester, which will shorten your time in college. It's also a good idea.
So, in a word, paying more attention to your study is the best way to save money. As for making money, in any case, as an international student, the work you do will not be very profitable, and most of it is just manual labor.
If you want to come to America, cheer up.