Build huge amount of backlinks or not neither the two will bring good results and completely have nothing to do with the age of the domain. Domain age is a big SEO myth. If a certain domain is aging 10 years without building any links or promotion to it (which is definitely impossible to happen) is just as valuable as a 1 month domain.
Regarding to your question, building links too many or not is not that important. Quality is the key. Google is now discounting links. You will not raise a red flag in Google's eyes in building too many links in a short period of time. But you will not gain something either unless you are able to build good quality and relevant links (which is again very impossible to do in a short period of time unless you will pay for it).
So better to take things smoothly or else you will end up crying.