Can someone who arrived to the US in their junior year go to college?

As you know, American universities are very, very expensive. Higher education is not treated as a right earned by academic excellence, but as a luxury good which can come in its low-cost/discounted/pared-down version. It is, however, open to basically anyone provided they find the money to pay.
There are 3,700 universities in the US. Only about 60 to 80 promise to meet 100% need for all students they admit*. Those universities are the best in the country. Even that if often a lot of money. Other universities don’t care what you can afford - they give you a quote and it’s your problem if you can or can’t pay. Living in California, you’re lucky, because there are State grants to supplement the universities’ and federal offers, and UCLA even has a special fund for the brightest lower-income students. All UCs are good, and many CSUs are quite good too. Colleges such as Pomona, Occidental, Harvey Mudd, are elite and meet full need, being very generous in their estimations. In short, CA residents have a lot of good choices if they can complete the most rigorous coursework and get excellent SAT or ACT scores.

That’s why your status is super important. As a refugee who’s going to be a CA HS graduate, you will be considered a permanent resident for federal financial aid purpose, you’ll be in the “domestic” application and financial pools, and you’ll be considered in-state for UCs and CSUs. That’s the best possible status for you.

I would recommend you dedicate one more year before you think of tackling college admissions. In the US, your application would require a variety of classes that you may not have and to be competitive those classes need to be taken at the highest level (AP or Honors) in as many classes as you can. Your teachers need to know you well so they can write meaningful recommendations. You need to be at the highest ELL/ESL class level, then be able to switch into AP/honors classes for those subjects. In addition, for the best options financially, you need to work on standardized testing methodically, in order to get the highest possible scores.
Doing this would allow you to compete for Questbridge, a national selection system that guarantees a 4-year scholarship to lower income students (since you’re a refugee, I assume you’re lower income.)

This is a website for first gen students, lots of useful links. Below, the list of colleges that meet 100% need.
http://blog.■■■■■■■■■■■■■■■■■■■■■/blog/colleges-that-meet-100-of-student-financial-need/