You will be billed once you account reaches its billing threshold https://support.google.com/adwords/answer/6311 which can be independent of whether you have or have not reached the number of clicks you have referred to. Please check your billing tab and options to see what this threshold is and when you will be billed. If you don't reach this threshold after 30 days you will be billed at that time.
To build upon the great resources Jordan shared with you, AdWords billing does not work on a clicks-per-month basis. You are charged for each click, and you will be billed once your account reaches the threshold Jordan mentioned.
Let me know if you have any questions!
You should first investigate which payment options are available for your country, here: https://billing.google.com/payments/paymentoptionfinder
Then, choose billing method that fits you best: https://support.google.com/adwords/answer/1704418
Either way, Adwords will charge you - per click. But to directly answer your question -- yes, Google may bill you even if your preferred monthly number of clicks isn't reached. There isn't a setting that ties billing in relation to "total number of monthly clicks", but you have plenty of options anyway.