Get to the fun, right away
Some games are very good at getting to the meat right away - they may have a team/mission dynamic, they may have a set scene structure/scene framing rules, or they might have a specific scene that starts every campaign.
When I move to more traditional games that don't have this, I forget that you actually WANT to get things rolling right off, and you find yourself with a slow session or two before direction happens.
If it's a party-based game, start them as a team. Put clear goals and mission goals right in front of them, right away. Don't waste time with people poking around trying to figure out what they should be doing. There's a reason movies/books try to get to the crux of the conflict early on.
Importing Other Game Habits
A lot of RPGs don't tell you how to structure a session, or a campaign. So it's really easy to become accustomed to taking ideas or methods that work for a different RPG and putting them into any other RPG you run.
Sometimes, that's great - it makes a game work better. Sometimes, though, it works directly against what the new game does. Take some time and think about what support this game needs BEFORE you run it, and make a conscious choice about what you're bringing in or not bringing in so you don't find yourself self-sabotaging the game unknowingly.