Is there any way to create a blank solution (.sln) file first and then add projects?

Yes, How to: Create Solutions and Projects gives an overview.

From the article:

Creating Solutions To create a new solution

1. On the File menu, select New and then click Project.

2. In the Project types pane, select Other Project Types and then select Visual Studio Solutions.

3. In the Templates pane, select Blank Solution.

4. Enter a name for the project.

5. To change the location of the solution directory, choose Browse and specify a new location.

6. Select Add to Source Control if you want to add the solution to a source control database or repository.

7. Click OK.

After creating an empty solution, you can add new or existing projects and items to the empty solution by using the Add New Item or Add Existing Item command from the Project menu.

For Visual Studio 2019 the steps are described in https://docs.microsoft.com/en-us/visualstudio/get-started/tutorial-projects-solutions?view=vs-2019#create-a-solution

• Open Visual Studio.

• On the start window, choose to Create a new project.

• On the Create a new project page, enter blank solution into the search box, select the Blank Solution template, and then choose Next.

Note: You need to make sure you open a brand new project, right-clicking and create new project will not generate the option to create a blank solution.

For Visual Studio 2013, it has changed slightly.
Searching 'Installed Templates (Ctrl + E)' for 'Blank' works, too.

To create an empty solution

1. On the File menu, click New and then click New Project.
2. In the left pane, select Installed, select Other Project Types, and then s elect Visual Studio Solutions from the expanded list.
3. In the middle pane, select Blank Solution.
4. Set the Name and Location values for your solution, then click OK.

http://msdn.microsoft.com/en-us/library/zfzh36t7.aspx