You can either assign Elementor templates to an archive, or you can create a custom archive using Views, but not both.
If you want to use Elementor templates, I don't see any way in the GUI that you can modify the query that retrieves the posts (except for a pagination setting). You would need to contact Elementor support to find out what is available.
I just wanted to post an update so that other people who are also looking for a similar solution don't have to struggle as I had to. In short, there is no easy solution or workaround to this issue because the problem is with the Elementor Pro Posts Archive widget itself.
Purchasing Elementor Pro was simply a waste of time & money. I realised they were not interested in listening to their clients.
Even though this issue has nothing to do with Toolset Types, I still had to come here and ask for help because Elementor team was not interested in resolving this matter.
I went ahead with the refund as I found them to be full of attitude.
Instead, I am now purchasing Beaver Themer because it allows me to achieve exactly what I want.