So what if it’s massive? He’s already proposed to make Canada the fifty-first state and that’s bigger than any country except for Russia.
I don’t think the USA has the capability to populate, control, and govern a country the size of Ethiopia, in a manner that will prevent colonization and expansion by neighbouring peoples, groups, and even state actors.
The USA is too far away, Ethiopia is too large, the terrain too rugged, East Africa too populous, and (of course) Trump’s power is too impermanent. Worse scenario is that East Africans (the oldest continuously settled area of the Earth by humans) undermine any of Trump’s efforts by just living/moving/migrating/etc. and local state powers just wait a few years until Trump is dead (while other state aligned powers grow in influence and cement themselves).
Do you think Trump will outlast East African people and their interests? Trump can talk a lot, but he won’t be able to project the power required populate, colonize, and control Ethiopia.
The biggest reason Trump would never want to colonize Ethiopia, even if it was depopulated, is simply that it’s in Africa. His racism is blatant.
Assuming we’re ignoring the physical damage that would happen I discussed above, and a land grab is logistically possible, what we’ll see is a mixture of reactions.
The disappearance is bizarre enough that some people would refuse to ever go near the old borders of Ethiopia. Whether it’s fear of god, magic, aliens, or random events of the universe, they’re just not going. But others will see only the opportunity, or weigh the opportunity as worth the risk. They’ll act first, and so have an advantage over those who delay action for whatever reason.
So the land grab wouldn’t just be a land grab, it would be a land grab carried out by the most impulsive or aggressive people, who lack any regard for the risks involved. Fun Times!
Trump would try to make a 51st state out of a territory located in Africa that’s surrounded by African countries full of Africans?
I’d sit down and think this one through for a few more minutes.
Here’s the Macguffin. I suspect this would be the first thing we (the collective rest of the world) would head for, to see if this artifact was responsible.
But Trump certainly wouldn’t. He’s proposed depopulating Gaza to build a resort.
Is a shithole country™ still a shithole country™ in trump’s view after all the inhabitants have vanished and can be replaced by white overlords? In other words: What’s in there for him?
To elaborate on my above point, I don’t think Trump would get past a gut-level revulsion of Africa and all things African. For him, Africa = black = disease = AIDS = poverty and there’s no way he’ll ever get past that. Conceivably he might propose building a wall around former-Ethiopia to keep it white, but everyone including him knows walls don’t work.
Gaza is mostly beachfront, while Ethiopia is a landlocked country. Plus it’s bordered by allies, and Israel is whitish, if not exactly white. So it’s a thing he’s willing to mull over. But more importantly, Trump is lying about Gaza. He’s never going to set foot there, he’s never going to invest in even a single paving-stone.
Maybe this observation is too literal for an obviously fanciful conversation, though.
Since we are talking about Ethiopia in such a flippant manner I decided to take a page from @Johanna and put on some Ethio-Jazz. And, of course, after a couple of hours I must share a wonderful Aster Aweke song/album.
Thank you! 
And here are the Israeli/Ethiopian fusion pop grooves of the Idan Raichel Project:
