Floating at the center of a gas giant without being crushed or melted by pressure and heat would be highly unlikely for most objects. Gas giants, such as Jupiter or Saturn, have immense gravitational forces and extremely high pressures and temperatures in their cores.
The center of a gas giant is subject to tremendous pressures caused by the weight of the surrounding layers of gas. These pressures increase significantly with depth as you move towards the core. The pressure is so immense that it can compress gases into exotic forms, such as metallic hydrogen, where hydrogen behaves like a metal.
Furthermore, the temperature at the core of a gas giant can reach tens of thousands of degrees Celsius due to the combination of gravitational compression and residual heat from the planet's formation. These extreme temperatures would likely cause most materials to melt or vaporize.
In such an environment, solid objects would likely be crushed and undergo significant changes in their physical state. Even if an object were somehow resistant to melting or vaporization, the intense pressures would likely cause it to deform or be compressed to a fraction of its original size.
However, it's worth noting that our understanding of gas giants is limited, and there may be exotic materials or structures that could withstand the extreme conditions at the core. But based on our current knowledge, it is highly unlikely that an ordinary object could float at the center of a gas giant without being crushed or melted.