Edge 830 Map Historic

Go to the settings of the routes in question and make sure they are set to always show.  Then they will appear on the map screen.

If you are referring to "Rides" that you have actually rode as opposed to following a "route" on the Garmin, then the answer is no. You can set the " history" colour but that will only show to where you have just ridden whilst riding. Once you clear the Garmin after that ride, that history will be lost and cleared from the map.

But, if you go into "history" and create a course of the ride you have just done, then you can set a colour to it and have it permanently displayed and that way will work along with as many other rides which you do the same to.

Otherwise, if you are just following a route, just do as the others suggest.

FWIW:  I don't see any utility in that on the device.  How would you use that feature?  Something like this is much better done on a website.

Main screen, hamburger menu -> History -> Rides -> [select your past ride] -> hamburger menu -> save as course.

Option names may vary as I have localized UI.

You can do this (or at least a similar effect) with a paid subscription to wandrer.earth