Sure it's possible, with Facebook paid ads...
I've gotten 18K likes in less than a week with Facebook ads.
I honestly don't trust others to do that for me though. Unless, they let me go into Facebook and see the actual ads they used, the cost per like, the people groups they targeted, money spent, etc.
If the likes aren't quality, they're pretty useless. Sure, it makes your page looks nice and popular, but you probably won't be able to connect with anyone of those "likes".
You would be better off learning how to get cheap FB "Likes" yourself through FB ads...
This is how I do it-
Keep it simple. Run 2 ads with the same text, but different pictures. Keep the one that performs best and then run that one against another ad with a different picture(same text). Keep the winner, repeat.
The same applies to the ad text. When you find a picture that performs well, keep it, and start making small changes in the text. Run 2 ads together with the same picture, but different text. Keep the winner, test it against another ad with different text, repeat.
I actually love testing ads like this because it's exciting seeing the results. You just need to be careful, because if you let the poor performing ads run for too long, you're Ad spend budget is going to get expensive.
Hope that helps buddy.