I’ll try to answer the question whether is it possible to speak a language like a native. I assume the question means: is it possible for a non-native to speak a language like a native, so that it would be undetectable by a native?
The answer is that if you begin being immersed in the language before age 13 (or maybe 14), you probably will.
However, if you are older, it is highly unlikely that you will ever be able to fool anyone into thinking you are a native speaker, or that you will ever be able to speak it without thinking about what you should say. Maybe, if you are highly motivated and willing to spend years perfecting your accent and acquiring vocabulary, it is possible for a teenager or young adult.
If we are talking about a person in their mid-20s or older, I’d say no.
For one thing, just the vocabulary alone is overwhelming. You need at least 20,000 words to have a native-like knowledge of English. Do the math. In 10 years of persistent study, you would need to learn 2,000 words a year (more than 5 new words a day) and not forget any of them. And after that, there are idioms. Of course, you know run, but do you know run out, run up, run away, run after, a home run, a run in her stockings, a good run on Broadway, and so on?
Plus grammar, plus phonology. It’s a little overwhelming.
A person could have a native-like accent, maybe enough to make an American think you were British or vice versa, and 2,000 to 3,000 words of vocabulary, and get through the basics of life. But to enjoy movies, enjoy novels, read the sports page, grasp political commentary, etc., is a high hill to climb, but it’s possible.
source text: https://www.lingq.com/en/learn-english-online