The translator is a native speaker of Japanese. He translated the title 70億人の頭の上に風船を as, If I Could Put Balloons on 7 Billion People's Heads. However, another old translator who was removed for an inaccurate translation is "If 7 Billion People could put Balloons on their heads" how would I know it's this conditional, does it have to be impossible? What if there was a crazy impossible lyric with a lot of numbers, with an omitted wo, would that be conditional as well?
「70億人の頭の上に風船を」↔ 'Balloons above 7 billion people'
The vocabulary 'balloon' makes the sentence quite poetic. It seems that the sentence intentionally omitted some verb to make the sentence looking even more lyrical.
Japanese people conventionally use the phrase 「頭の上」(above head) as the meaning 'above'(direction) to distinguish it from just 「上」, which can be interpreted as having various meanings. (Rank, above your chest, upon some condition, etc.)
If I make the number crazily larger and omit 'wo', then the sentence looks like the following.
「千億人の頭の上に風船」↔ 'Balloons above 100 billion people'
Now the sentence, in my opinion, becomes much less poetic. Also due to the unrealistic number and absence of a poetic element of the sentence, the atmosphere the sentence gives me is quite dystopian.
As regards your question about the 'condition', I don't get it how can a sentence of [70億人の頭の上に風船を」can imply 'If~~~' as its meaning. To imply 'could~~~' or 'if~~~' in a Japanese sentence, some words like 「もし」,「かもしれない」should be included. Maybe there was some confusion on your part while communicating to each other.
Edit: After knowing the context(context like 「頭の上に風船をつけて」), now I may change my opinion on the sentence.
「70億人の頭の上に風船を」↔ 'A balloon upon each of 7 billion people's head'
This sentence is intentionally omitting the verb 「つける」, which could have been directly meaning 'attaching a balloon to each of people's head'. However to make the sentence more poetic, it omitted the verb and it is allowed in a Japanese sentence for those who know the context.
In this case, considering the context,「頭の上」attains its meaning as not just 'above'(direction) but 'upon head'. Since it is implying its intention to attach something(which is a balloon) on the head.
This is a title of a song which should be lyrical, and people who enjoys the song should already have been knowing the context.
So even though the word 「つけたら」('If someone attach something on something') has been omitted, it is fair enough to translate the sentence as "If I Could Put Balloons on 7 Billion People's Heads". It is because when we translate a language to another language just literally, without considering its context, we see often that the translation ruins the atmosphere of the original sentence.
If I were a fan of the song who wanted to translate it
'A balloon upon each of 7 billion people's head'
'If I could put balloons on 7 billion people's heads'
even I would choose the latter one since it is conveying the intention of the sentence more rightly. In many cases of translation, such as when we make some subtitles of movies or animes, we observe a lot that those subtitles choose to convey the atmosphere of the sentence rather than just translating it literally.
The translation you've posed on the question is the case which chose to convey the atmosphere of the sentence than just translating it literally.