This issue seems not to be related to Sitefinity itself as the error you are seeing basically says that Sitefinity cannot connect to your database server, which could be caused by variety of reason.
1. For example the database server could be behind firewall (e.g. if it resides on another machine).
2. Based on our experience this issue may also occur if there is no SQL Server installed on your machine where you try to create the Sitefinity project.
3. The other possible reason for the issue is if the default SQL user on the machine doesn't have rights to create new databases on the MS SQL server or SQLEXPRESS.
In order to resolve this issue, please make sure that you have installed a supported version of SQL or SQLExpress on your machine and grant the process running Sitefinity or Sitefinity Project Manager Create database permissions.
Please refer to the following article for more details about the Sitefinity prerequisites:
4. In addition to that this issue may also occur if the SQL Server instance is not started / running, or in other words, Sitefinity cannot find your SQL instance to create the database. Can you please make sure that the SQL Server instance is started / running on your side?
You may also refer to the following article from our documentation for more details about configuring a Sitefinity project (please refer to step 2 for more details about setting up the database and the requirements):
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