First thing you'll want to do is progress through the story until you reach tangaroa, that's when titanium really becomes accessible. The residential areas there have some good spots but remember to bring a machete since a lot of the best routes are blocked by overgrowth. Metal detector is going to be your main tool here, you'll want to use it extensively to find those safes with 3 ore and briefcases with single pieces, and the timing between scans is pretty quick so you can cover ground efficiently.

Trading posts are actually really reliable once you've got your reputation maxed out, they'll give you 3 titanium for every 3 trash cubes plus 1 trade coin which adds up fast. Each post stocks about 15 pieces, and there's a nice rhythm you can get into where you're converting extra resources into cubes while fishing for those coins. The sweet spot is hitting multiple posts in sequence, since their stock refreshes independently.

For maximum efficiency, you'll want to sweep each new island with the detector first, focusing on flat areas where treasures tend to spawn more frequently, then work your trading route between posts. Once you get the timing down on the detector sweeps and post visits, you can maintain a pretty steady supply for all those late-game blueprints and batteries you'll need.