First of all, when you post a question like this, we will have to do quite a bit of guessing, because there are so many alternatives.
You say that you downloaded SQL Server, but are you really sure that this is what you downloaded? A mistake we see every once in a while, is that people download SQL Server Management Studio, SSMS, thinking that this is what they need. But SSMS is only a tool to talk to SQL Server. And if you are in a corporate environment and there is a SQL Server instance on the network, SSMS may indeed be all you need.
But if you are working in your own private laptop, you need both SSMS and SQL Server. You find downloads for SQL Server 2022 here: https://www.microsoft.com/en-us/sql-server/sql-server-downloads.
There are several other alternatives, but I stop here. If the above does not help, please provide more details about your environment and why you expect the connection should work.