Selflessness as a leader can often inspire selflessness in others. I was lucky enough to work for someone for nearly twenty years who was always the first to give and sacrifice for the sake of the group. He was generous in ways that really cost him, and, partly as a result, he inspired intense loyalty and dedication. It is easy to work for a boss like this. He was also immensely trustworthy.
There's a lot of things you could do. You could try to do a few social things like all having lunch together. You could try to assign tasks at first that force the team to work together in different combinations so that everyone ends up feeling connections to everyone else.
encourage and facilitate good communication within the team as this will bond the group into a more effective group. Also allow autonomy or discretion to all members so as to fully maximize all their diverse expertize and in the process, each team member gets to learn new skills and this will lead to success in the organisation. Carefully design a appropriate chain of command and functional groups