I suspect this the great misunderstanding as far as Trump is concerned. He is not a politician, doesn't think like one, and is proud of that fact. In the US one or two are now beginning to wake up and see this is the case, and the rest of the world, now including Iran, are perhaps beginning to wake up to this fact as well. Trump doesn't really worry about losing face in a political sense, unless it scuppers his deals. Why has Soleimani been taken out now, if it was a political risk before, why now, what has changed?
In Trumps view, the pressure on Iran has to be increased to get them to the point where they will negotiate on his terms. He has done the same thing with China via the trade war scenario, although not using such naked force because after all China is a different story to Iran.
Trump wants to win, if he cant win he'll take as many cents on the dollar as he can get, if that's not possible he will walk away and come back when the signs are better, or when he can apply more leverage. If that never happens he shrugs his shoulders in a "you cant win them all manner."
Appearing not to give a feck is all part of the Donald's play-book and he's not really worried about any collateral damage caused outside America, whether its to friend or foe alike. Yet you suspect he would like a place in history, even if its the notoriety of being only the third USA President to be Impeached whilst reasserting America's place in the world as the 'big guy on the block' and not to be messed with!