It is always the expectation of those charged with the task of training or managing you that early-on you will start slow and be an impediment to the company. If you can figure out a way to violate that expectation, e.g. produce something meaningful in your first 1-2 weeks, you will have made a good impression that will last for a while. Build on that impression.
In my first "bigboy" job, a nine-month contract-to-hire gig at a very well known financial, I failed to violate this initial expectation. I did great work there (eventually) but was still not hired full-time because my slow start left lingering questions for a few key people that were never answered.
Some managers fought to keep me, but it wasn't enough. On the day I was terminated, my manager told me that the one piece of advice he would give me was that wherever I go, make sure to kick ass right away. I've followed this ever since and it has paid huge dividends (constant, rapid promotions).
Always be delivering value.