No, this is not the best way to handle a db connection. You only want the db open and around for as long as necessary and no longer. Usually this means opening the db connection at the place in your code that can know how long to keep it open and then close the connection after using it.

If you are simply referring to the configuration for opening a DB connection, then you could define that configuration object at application start and then pass it as a parameter to your db instantiation code.

import myUserDbCode from '../myUserDbFile';
import myUserMessagesCode from '../myUserMsgsDbFile';

const dbConfig = {
  dbname: 'myFancyDb',
  serverName: 'myDbServerName',
  connectionTimeout: 60
}

(async () => {

  const userList = await myUserDbCode(dbConfig)
    .then((dbResultSet) => {
      return dbResultSet.data;
    }
  };

  const myUser = userList[42];

  const userMessages = await myUserMessagesCode(dbConfig, myUser)
    .then((dbResultSet) => {
      return dbResultSet.data;
    }
  };

  console.log(userMessages);
})();

I recommend following some DB tutorials that show how to build a complete application to see some patterns about how to handle passing configuration options to code and how to manage DB connections.