Mounting PVC to pods in a cluster dynamically

I’m a beginner using kubernetes. Recently, I tried to build a platform for data analysis, and the platform was running as a deployment in a cluster. The data that users wanted to analyze was mounted to the deployment.
Here is the question, since there are so many data and users only want to analyze a few of them, they will choose the data they want in the frontend pages. After users choose the data, I will mount the data to the running deployment. As far as I know, if I mount a pvc to a deployment, the deployment will be restarted and upgraded. However, if the analysis programming is running, restarting the deployment will interrupt the progress. This is not what I want. Is there any way to mount PVC to pod dynamically without restarting and upgrading the pod?Just as Kaggle has done, adding datasets dynamically

Thanks a lot!