Team building is a very important challenge to tackle even before you begin thinking about building robots. On my team specifically (148), we try to knockout two birds with one stone wherever possible by using simple and fun design challenges as team building exercises. This gives students a chance to start developing a problem solving skill set all while getting to have fun and meet their fellow team mates.
Here is a link to a video of a Pumpkin Chunkin' contest we held one preseason:
https://www.youtube.com/watch?v=gOgdZGcj9_I
We were able to divide team members up into groups that included a good spread of rookies and veterans as well as a few mentors. While the size of this event may not be what you had in mind, it can certainly be scaled to fit your needs. Competition is also a great force for bonding, as we can all attest from years of FIRST involvement. Congrats on your appointment, and I hope this can help you think of some great ideas for your team.