Many people learn to be fluent and almost bilingual by learning a language as a foreign language rather than being immersed at a young ago. So it is doable.
My 8 year old son has been studying Mandarin as a foreign language for 3 years now. For the last 18 months he has been doing the following:
Whilst brushing his teeth, showering, and getting dressed and undressed in the mornings and evenings he watches or just listens to Mandarin cartoons on you tube. This amounts to about 30 minutes a day.
He has 30 minute on-line lessons on Saturday and Sunday. During holidays he frequently asks for more of these so last year, despite some lessons being cancelled for holidays, he still did over 110 of these. He even did some of these lessons when we were away on vacation.
I used to also play CDs in the car as well, but have decided this is overkill and that learning a language is a marathon and not a race.
His school also does 1 x 30 minute lesson a week. The level of this class is much lower than his, but he does like being the best in his class so this does give him an added incentive to learn.
I am not saying that the above is perfect, but I believe he has very good pronunciation in Mandarin and within a few years he will be fluent. This does not mean that at 11 he will be the same level as a native speaker, but he will have a very good base to progress to a very high level in the future.
My son's level of Mandarin is the highest in our household and he never gets to speak to native speakers outside of his on one .
I have been in the language teaching business for over 20 years so am reasonably confident that he will get to a very high level in Mandarin as long as he can keep motivated.
Also, reserach shows that Mandarin takes a lot longer for native English speakers to lean than Italian.