Recently, there has been a trend of designing neural data structures to go beyond handcrafted data structures by leveraging patterns of data distributions for better accuracy and adaptivity. Sketches are widely used data structures in real-time web analysis, network monitoring, and self-driving to estimate item frequencies of data streams within limited space. However, existing sketches have not fully exploited the patterns of the data stream distributions, making it challenging to tightly couple them with neural networks that excel at memorizing pattern information. Starting from the premise, we envision a pure neural data structure as a base sketch, which we term the meta-sketch, to reinvent the base structure of conventional sketches. The meta-sketch learns basic sketching abilities from meta-tasks constituted with synthetic datasets following Zipf distributions in the pre-training phase and can be quickly adapted to real (skewed) distributions in the adaption phase. The meta-sketch not only surpasses its competitors in sketching conventional data streams but also holds good potential in supporting more complex streaming data, such as multimedia and graph stream scenarios. Extensive experiments demonstrate the superiority of the meta-sketch and offer insights into its working mechanism.