No, putting something in the freezer before melting it will not help it freeze faster. In fact, it will have no effect on the overall freezing process. The reason for this is that the rate of freezing is primarily determined by the difference in temperature between the substance and the freezing environment, not the starting temperature.
When you put something in the freezer, it will eventually reach the same temperature as the freezer itself. Once it's already at the freezer temperature, melting it and then trying to freeze it again won't speed up the process.
For example, if you place a container of ice cream at room temperature (let's say 25°C/77°F) directly in the freezer (typically set to around -18°C/0°F), the ice cream will have to lose 25°C/77°F of heat before it reaches the freezer's temperature and starts freezing. If you instead put the ice cream in the freezer first, it would still have to lose the same amount of heat to reach the freezer's temperature, whether it's frozen or not.
If you want to freeze something faster, it's best to spread it out in a thin layer or smaller portions. This increases the surface area exposed to the cold environment, allowing heat to escape more efficiently, and speeding up the freezing process.