Kills, exploration and discovering area. If you haven't gone to the other starter towns, go there and get the locations like Sawmill and Warehouse, or the motel and store between the town and the base.

There's some random points around the map, usually around bigger crossroads, that give a little xp when you discover them. Otherwise once you're out of tasks for now the only real way is grinding military enemies in high tier areas: TB, FN, MS.

If I am not mistaken, killing tier 1 enemies (from starter town) gives 5 XP per kill, tier 2 gives 10, and killing tier 3 (LAF/military) gives 15.

My go-to places for XP are Fort Narith Barracks for the loot and Tiger Bay UNLRA container loot (plus the food crate there) so I can also get some rare loot along with XP

Use map geenie and hit all the small POIs on around the world for XP. It'll turn into a walking simulator so bring extra food/water. Also going to MS and TB and killing around 700-800 enemies will bump you up. Its a grind though, took me forever to get to lvl 37 after I completed all the tasks.