In normal and non-mayhem, the maps are “locked” to whatever level you were when you first entered them, with a few exceptions. This means that everything in that location (enemies, loot, vending machines, crew challenges, etc) will stay at that level.
If you’re below the recommended level for the main story missions, the maps get locked to the recommended level, I believe, and sanctuary gets reset to your level every time you enter it. There’s a couple of missions that reset the level lock on maps too, like when you kill the second mouthpiece.
So in answer to the original question, yeah it’s doable, even without mayhem, though it might be tedious. You’d just have to do every side mission as you went and explore every map thoroughly, before moving on, so you max your level and the next map gets locked to a higher level. If you’re avoiding mayhem, grab every crew challenge as soon as you can (otherwise save them for level 65 M10/11).
To be fair, even if enemies are underleveled, you can still get xp from them, for a few levels, so if you struggle you could replay maps a few times to level up more before moving on.
However you do it, Good Luck and have fun. =]