tiawd, we have a CHELEK Elokei, we are not God, we were given are PART OF God when He blew our neshameh into our souls and we are a part of Him as long as we exist because of His being the Source of life at every moment of our existance. So while it seems like a paradox, in reality it is not.
The definition of emanate means to spread out from a single source. So if we emanate from the Source which is Hashem then aren’t we part of Him? And yet, God is One and we are not God. But not only us, all matter, which equals energy, gets it’s energy from One Source, God. So in essence everything is an extension of Him.
In a similar way, children genetically have parts of their parents but they are not their parents, they are seperate individuals. This analogy is different from God and Jews, or all matter, as we have a soul provided by One God as opposed to two parents, and that we must continually rely on God for continued existance unlike parents whom we can become independent of. But the point is that we have parts from others yet not be part of them. With God we are always part of Him as we cannot become independent of Him as we are from our parents.