Last I checked, not with StreetComplete. But the OSM wiki has a table of Android apps https://wiki.openstreetmap.org/wiki/Android which column "Record tracks" can be sorted by, to see which apps have that feature.

How I've done similar before is to record a GPS trace with an OsmAnd plugin, upload it to OSM servers, import it as an overlay in the web-based editor on desktop, and used that and satellite imagery as reference to draw in the missing trail.

In a pinch you can also record a trace and edit directly on it in the field with the Android app Vespucci, but its UX is clunky and much less friendly to new contributors than the web-based iD editor.

If you are in the U.S. please each out to OSMUS, they are amazing and can connect you with trail mapping resources. There is a vibrant community of folks keeping our trails mapped!

https://openstreetmap.us/

As the other commenter mentioned the web editor is probably the most beginner-friendly editor. It might seem a little daunting but it's actually not that difficult to edit OSM. When you save your change there's an option to request a review of it. That'll get an experienced contributor to take a look at it and help clear up any mistakes.

OSM also has a public database of GPS tracks that contributors use to aid in mapping. Even just walking the trails with GPS tracking on and then uploading the tracks to OSM without doing anything else is a valuable contribution that will allow other contributors to map the trails at some point in the future.

You can edit existing trails, but directly adding new ones is not intended. What you can do is create a GPS track, and then upload it with a note describing the problem.

I use the app Vesspucci for actual editing, it works well (but larger changes to OSM is a "full PC" kind of task). Notes from StreetComplete (from all users) show up on a TODO list in the app, so the more advanced users can decided on whether they want to create a node on the map from the note.

You can record tracks or add places right in the app.