Trying to gain the trust of one person so they can help you influence the rest of the team may seem manipulative. That’s because it is manipulative. You may have been told that manipulating people is a bad thing to do. It isn’t. Exploiting people is a good thing, but only if you are open and honest about it.
When you find one person to be your advocate tell them that is what you are doing. Explain that you aren’t as close with the rest of the team as you would like to be and you are hoping they can help. Ask them for their advice. Let them know that you hope they will help you improve the level of trust the team has in you.
Manipulating people is seen as bad because it is often nonconsensual. The person being manipulated doesn’t even realize it is happening. When you ask someone for their help as your advocate then you are informing them and asking for their consent. Asking people for help is a good thing.