Pre-Trim Video Before Import?

Yes it does say MP4.  But, I had my hopes up that maybe it would have a little wider application and be more useful.  

mp4joiner didn't work very well.  I got it to join two 4K MP4 clips from a Panasonic camera.  It would not split a clip from the same camera.  It would not recognize MOV clips from an Olympus camera.  It was a good idea, but it won't be useful to me and I uninstalled it.   

YES! ...Yes if the file is a mp4...https://www.mp4joiner.org/en/"

Thank you Ann!  You've given me a project for my self quarantine time!  I'll try it out today.

YES!

Can you do it in some other simple freeware program?

Yes if the file is a mp4

https://www.mp4joiner.org/en/

Is there any way to do it without re-compressing?

Its without quality loss.

What you see doing editing is a "best that your computer can do" preview.  While you edit you are making markers.  During output the source files are read from scratch, interpreted and put into a new file using the instructions you give the program.   "Rendering" is a very confusing word that probably has a precise meaning.  But it gets used in so many ways, it is not always useful.  Words like "coding", "transcoding", "processing", "rendering" and more get wrongly used.   "Re-compressing" like multiple resavings of JPEGs is logically applied to video editing.  

No, not in PrE.

No, not in Organizer

No, none that I've ever heard about that's free.  

No, not if you find a way to actually cut the file.

Yes, it has the odd name of "Smart Rendering".  A company called Pegasys has one that gets pretty good reviews.  For $70 (??) you can buy "TMPGEnc MPEG Smart Renderer 5".  It is advertised at editing video without encoding.  That doesn't work well for most people.