Just some thoughts....
I am bilingual, english being one of the languages. I've read in many psych books that the brain learns pronunciation and patterns in infancy and very early childhood.
(and based on my life experience I fully back that up)
So I experimented on my son, the "control group" is basically everyone who has not done this. Not a well designed experiment, I admit :)
We listened to chinese, japanese, arabic, slavic and latin based songs, speech when he was really small.
Most of what he heard from me was in English as a baby. Rhymes, song, etc. Partially because of the above, and partially because I knew them better than the others.
We have always talked to him -from the point of him starting to speak -at 11 months old (too soon :)- in our common mother language with my husband.
All through his kindergarden years he has heard me speak english to him, but never responded in english or shown any signs of particulary understanding it. So I just declared the whole experiment a bust. And was quite disappointed as I would have liked him to be bilingual as well.
We moved to London when he was 7 and he started school here. With 0 english knowledge. And here is the interesting part: in 3 months he learnt to read/write and speak english to the extent that he was -by month 5- put into the gifted group in english.
Another interesting (1) thing that surfaced a few years ago that when he started watching anime in japanese (most only have subs, not voiceovers) he could discern the words and "hear" the words separately. Even though his exposure to japanese last was when he was about a year old. I have been learning japanese for a little bit now and I still have trouble finding where the actual word starts/ends in real life speech.
(2) Europeans usually struggle with a few very specific arab sounds. It is just foreign to us to create the sounds in our nose or at the back of our throat. He has no issues with this. Has no idea what he is doing obv., but he can easily mimic it.
Apart from the identification and mimicking of sounds I think exposure to all the diff language patterns have helped him a lot. In his opinion he is rubbish at languages, but all his teachers (french and german) say that he is really amazing at them. But being a perfectionist yet totally lazy teenager makes him believe otherwise.
So 15 years past the initial 'it's a bust' I do think we have given him an advantage.
On the control group thing: We have some acquaintances who came from the same country as us, non bilingual, didn't do anything like we did, have the same aged kid(s) and their kids -in general- took about 7-11 months to be proficient in english.
But by now (10 years on) most of them are truly bilingual.
In my opinion - even if you only expose your kid to other languages it is already a big thing forward. They will have the option to use that subconscious knowledge or not. If GPs are in the picture on a frequent basis than chances are your kid will learn their language.
Other side of the coin: see the "control group" they are just as fine, just took them a bit longer to get there.