First impressions can be a lot of pressure. The goal is usually to get the other person to like you, and being nervous can have the opposite effect. For a calm, warmer first impression, assume the person already likes you.
It's referred to as social optimism or the acceptance prophesy, and research supports that it's effective in making a good first impression. In a study titled Deconstructing the "Reign of Error", researchers hypothesised that people behave more warmly and friendly when they expect to be accepted. In turn, they exhibit behaviour actually results in their acceptance. To test this, they studied a group of men and women and their first impression interactions. They convinced one group of men that there was less risk of being rejected, and then they studied the men's behaviour and asked the women what they thought. Ultimately, here's what they concluded:
...we tested our hypothesis that a thin slice of warmth is sufficient to explain the association between anticipated acceptance and actual acceptance. Results strongly supported this hypothesis, demonstrating the interpersonal power of being warm and friendly.
Keep in mind, this is one small study, and it's with one specific type of interaction. Still, the takeaway makes sense: if you're not worried about being disliked, you'll probably be a lot more relaxed, calm and optimistic. Generally, people respond better to that behavior.
Of course, like any tip, this one can be taken too far, too. If you do or say something the other person doesn't like, they're probably going to dislike you even more if you ignore it and pretend they love you and everything you do. It's more of a tip for easing nervousness and getting yourself to open up in the first place.
And aside from making a good first impression, it also simply helps with your own well-being. If first impressions make you anxious, approaching it as though the person already likes you is a good way to remain calm. Check out the study for yourself.