How to create n number of database connections on the fly?

I'm trying to implement a dashboard (web application) where user could able to connect to their own databases and run the queries to build visualizations. Since the option of connecting to database is unknown to me, I'm not sure how to handle the database connection on the fly. Note that I'm not using any tools such as Hiberante etc. I'm on plain JDBC.

I can understand that creating a database connection is costly, so not sure how to handle it if say for example there are 200 unique visitors to my dashboard who connects to their own database and running queries! How to handle such scenarios?