SilentSoul89, I first want to compliment you for being a volunteer anywhere. You're a step ahead of where I want to be myself. Allow me still to offer these comments on your experience.
First, it does take time to become part of a click, and the longer you stay with your volunteer group, the more you'll become a valuable part of it. This will become more apparent as senior members move on and newbies come in behind you. This is a process that occurs everywhere - you invest time and effort, and it slowly pays off dividends. So stay with it. Unless you find your time better spent elsewhere, you probably will inevitably form some good working relationships there - friendly acquaintances that you'll enjoy interacting with each week. This should have you coming home afterwards feeling good about the day.
Second, while time with your volunteer group should yield friendly acquaintances, your goal should be to turn one or more of those acquaintances into a personal friendship that goes beyond the volunteer work day. Achieving this may very well depend on you being the one to reach out. As you spend time there talking to everyone each week (which you need to proactively do so that people see that you're a friendly person they like), you should have a feel for which ones might have compatible friend potential. Making the jump from routine work contact to outside social encounter is a critical step that we usually just don't do. It takes determination and effort. That though, is what starts a real friendship - which is a solid treatment for loneliness. Set yourself a goal to ask someone out to share a place or activity - suggest a specific date and idea for something. When I was climbing, I made 2 of my best permanent friends by initially inviting them out to give the sport a try. Biking, kayaking, road trip to a nearby park, a movie, or dinner with 2 or 3 of them. Whatever it is, you must make the effort to find out the interests of others, share your interests with them, and see what possibilities open up for getting together to share something. Assertiveness is the key ingredient. So, if people there aren't showing enough interest in you, you need to compensate for that with your own dynamic, friendly, outgoing personality and efforts. Reach out to them, find common ground, and propose a specific get together that might start a friendship. If one doesn't bite, find another. There may be someone else there, like you, who could use a personal friend, but just isn't socially confident enough to break the ice with you.
Third, I bring up a Christian doctrine relevant to your situation. I understand you wanting to feel more accepted there and to ultimately obtain some worthwhile relationships that end your loneliness. That's fine and something you may work on for many years to come. Some of us spend a lifetime working on it and never find complete satisfaction in our relationships. There's an important point to realize here though - that your joy in life should not be entirely dependent upon being accepted by others. I believe that our entire purpose in this life is to know and love the Lord first, and to love and serve others second. That means that focusing on God and others is more important than focusing on ourselves. Thus, our desire for recognition or acceptance, though nice, is not really important in the big scheme of things. So let me tie this point specifically to your situation as a volunteer. Assuming you are in fact helping children in a Godly way, your work of volunteering is a worthy act of love. You're serving the Lord by serving others. That alone is cause to add peace and joy to your life. After going home from a day of helping the kids as a volunteer, you need to consider and appreciate the good day that you've given them. You didn't waste it, and you probably had some good impact on a certain kid that you may never even know about.
So, I encourage you to assertively work on the relationship potential with the other volunteers. That can bring some worthwhile happiness into your life. But seek your inner peace and joy from who you are, what you believe, what your values are, and what you do with your life. Your "giving" as a volunteer is a part of that, especially if you can have a positive influence on impressionable youths. If you can focus on making each day purposeful towards loving God and others, you'll come home from your volunteer days feeling happy, regardless of your own life's deficiencies.