"Los niños ya comenzaron."
Translation:The children started already.
los niños ya comenzaron means, the children already started or already began.
to say your answer, have started/have begun, it would be los niños ya han comenzado.
They are two different forms of the past tense in both Spanish and English, and are not interchangeable in either language.
Not sure I understand what you mean when you say they are not interchangeable in either language. One wouldn`t use " The children already started " in British English, so there is no alternative there. Whichever of the 2 examples you give in Spanish would be the same in B English.
I agree here, that in english you simply don't use "the children already started". It's grammatically correct, but it does not make sense. If you say: "they started" it's in the past, which means that the action was started in the past and it's already over. So it's pointless to use "already", which relates the action to the current moment. However, if you use present perfect, that is "they have started", it means that they started in the recent past, and the action is ongoing in the present. So it is meaningful to relate it to the present moment, which is reinforced by the word "already". I suspect that in spanish it may be a bit different, the three past tenses do not have such a clear meaning distinction (although I guess they did have in the past, but it faded out), especially if you consider that they use it differently in different areas of spain, and even differently in latin america.
"The children already started" makes sense in American English at least. --- Someone shows up on the scene, "Alright, let's get started on that project." "But the children already started!" --- Sticking a "have" in there also works for us but can sometimes sound awkward depending on the circumstances. But if it really never works without the "have" for British English, then it should probably be accepted...
The problem with translating this as "The children have already started" is that it is in the wrong tense. The sentence is written in the simple past/preterite tense, and adding the "have" turns the sentence into the past perfect tense. These are different tenses in both English and Spanish and mean slightly different things. Since the Spanish is written as "comenzaron" instead of "han comenzado", "started" is correct and "have started" is not.