Getting along well with your whole team is a laudable goal, but it is easier to connect with individuals than groups. There will always be a couple of people on the team who you connect with more than everyone else. Find those people and cultivate those personal connections. Having closer relationships with individuals within your team will make you happier with your job and help build trust.
Trust is a tricky thing. Exactly how and when one person begins to trust another is very difficult to define. You need to get your team to trust you, but this a slow and gradual process. Start with just one person. Go the extra mile and give that person a reason to trust you. Then give them a few more. Once that person trusts you they can be your advocate on the team. They will help other people trust you.