Making 1 bitcoin with zero balance and in one month. Its going to be pretty hard, unless you get lucky on some gambling sites or trading. But for that you would need to spend a lot of time on the faucet sites.
If you are looking to earn 1 btc only from faucets sites then it will take long time and not sure when you will get that amount in your wallet and your electricity and internet cost will exceed then your income which doesn't make any sense to me.