@yesh interesting question 
I can’t think of a solution to use dashboard with a drop down list allow user to select and preview table
But I can think of another solution, please see if it works.
If yes, please mark as solution.
You can create 7k datasets by using API CreateDataSet - Amazon QuickSight
And grant your user access to view this dataset and create new analysis. The benefit is your user is able to pick any one of the 7k datasets to view the data by creating analysis. It’s not as user friendly as a filter in dashboard but also not a very difficult steps. you may refer to the steps here Tutorial: Create an Amazon QuickSight analysis - Amazon QuickSight
The dataset can be grouped into different folders like what @Sanjeeb2022 has mentioned, it helps user to find out the related dataset and better for governance. You may govern the access by folder instead of individual dataset. You may also govern access by user group
Downside is all users need to be Author instead of Reader which increases the cost. But QuickSight’s cost is cheap. You may refer to here Amazon QuickSight Pricing - Business Intelligence Service - Amazon Web Services
And there may had a chance that users have created many dummy analysis and don’t clean up. You may use API to automate this clean up process DeleteAnalysis - Amazon QuickSight