Greetings, If you want to say something which happened early morning but is effecting our present moment then it is right. The baby has finally come early this morning. If you want to let someone know about the arrival then you can say- The baby arrived/came early this morning. Hope it would help ! Regards, Deepika Mantra

Do you mean that there was a birth this morning? If so, you would say: "The baby finally came/arrived early this morning." You have identified a specific past time so we need past simple.

The baby finally CAME early this morning. Could I ask any citizens of the US of A if they might be tempted by the present perfect here?

"The baby has finally arrived" or "the baby arrived this morning". But ''the baby has arrived this morning" is poor English (forgive me, native English speakers). When an exact time of an action is known, the perfect tense is not used.

I didn't see anyone comment on this, but otherwise the answers are great. >> "Finally" + present tense is never correct. "Finally" implies something that has occurred. You must use some form of past tense.