I think he played it just on time. It was a symbol that the U.K. are friendly and acting in good faith. The audience for the gesture wasn’t Trump but other international leaders and the populations of friendly countries.
It was a signal that the U.K. government is behaving in an open, friendly manner and that they are willing to talk. When Trump rejects this it will be his choice and therefore his fault. It’s international relations 101. It’s exactly what Trump doesn’t understand.
Starmer has an eye to negotiojs with other world leader. He can legitimately say ‘Look, we tried and he’s proved himself a mad man.’