All good and truth comes from God. He said: “...I am the light, and the life, and the truth of the world.” (Ether 4:12)
God is so good that he radiates goodness to everyone, whether they have heard of or believe in him or not. Every breath you take and every ability you have is a gift from God, freely offered, without so much as a need to recognize him.
Humans are not, by default, good people. This is due to our nature, which is selfish and carnal. All good things come from God: “...good cometh of none save it be of me.” (Ether 4:12) God’s good influence is constantly broadcast to all mankind in the form of inspiration to rise above the norm. These ideas can lead to a great deal of change in a person. Many have mastered the ability to listen to this influence, and have affected a great deal of good in this world, and many of them have done so without attributing this influence to God, or even recognizing it as external.
So what do you have to lose by limiting yourself to an anonymous God? Consider an analogy. If your purpose is to gather water, you can do so to a great extent by collecting rain in pots and collecting the dew from flat objects. But if limited to these incidental events, you can never generate water on demand. You are always subject to the weather or time of day and whatever quantity of water that happens to fall. Now imagine that you discovered a spring. At any point of the day you can collect water without any limit on quantity.
God’s truth is all around you, all the time, and you have access to it. Not accidentally, he describes himself and is described as a fountain of truth. “Therefore, with joy shall ye draw water out of the wells of salvation.” (2 Nephi 22:3)
In spite of the limitless nature of truth, those who do not recognize God as the source of it are limited by their perception. Without believing in God, you can’t trust in God. Without trusting in God, there are a great many things you will never notice, recognize, learn, and be that are good, because they will not seem good to you given your present disposition and awareness. When it comes to this set of knowledge that lies beyond what you would otherwise seek and gain, it is the belief in his goodness and a recognition of his being the source of the new thing that makes it desirable to you. You can bypass the limitations of default truth by accessing God— the source of all truth—explicitly.