Change ratio from 4:3 to 16:9 while keeping the whole width

As you start your project set your Video Mode (Settings/Video Mode/Custom/Add) to 1600x900.

You don’t have to have black bands, but you are not going to retain all of the video without stretching, which is why the crop tool was mentioned. It’s either cropping the video, or black band/bars.

This topic gets discussed quite a bit in here.
Here is a good thread to read through showing what you can do: Black border issues when using clips that contain different resolutions - #2 by Hudson555x