Is it possible to active this tower?

The existing tower? No.

You need to build a settler recruitment beacon if you want to complete that particular minuteman mission... at least that is what I assume... I am not going to bother building the beacon until I finish building and fortifying the settlement itself.

All you need are the components to build the beacon and copper to attach a wire between the beacon and the generator which already exists. I assume the workshop has all the components you need. I can't be positive because already dumped a lot of junk / components in that outpost's workbench.

The bench doesn't QUITE have all you need to build the minimum defenses required for the quest. At least, it didn't for me.

For new settlements that had no population at start, I build at least a couple beds (if there aren't any already present), some crops, and have at least one water pump. Then comes a generator and broadcast tower. Then go back to working on whatever needs to be built. Within a few minutes, the first settler will arrive. Assign that one to a Supply Line to your nearest other settlement. That almost (if not) immediately makes the resource material stockpile available for building up this new settlement. Generally, that provides enough materials to build the settlement up to at least mid-size capacity. (Beds, Food, Water, Defense, Happiness.)