No. For it to be solid the atoms would need to be locked into position relative to each other. The sun’s core is a plasma. While it is under intense pressure that keeps all of the atoms close together they are still able to move relative to each other. They pretty much have to in order for the nuclei to get close enough and fuse.
It is incredibly dense though. About 160 grams / cubic centimeter. Which is over ten times more dense than the solid core of the earth.
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