I can only find one instance of αββα in the LXX. It is used in 2 Chronicles 29:1 to render the name of Hezekiah's mother, "Abijah". The Hebrew word in this place is אֲבִיָּ֖ה (Strong's H29, Abiyyah), which means "Jehovah is my father" or "Yah is my father". 24 times prior to this, the LXX used Αβια for this name.
It seems reasonable to me, highly likely even, that the translators preferred Αββα in 2 Chronicles 29:1 in reference to Hezekiah's mother, because Αβια is masculine, whereas Αββα is gender neutral.
So, the use of Αβια -- "Yah is my father" -- transitions via the name of Hezekiah's mother, to "Αββα", and then 150 years after it appears in the LXX the word falls from the lips of Jesus in a most intimate appeal:
Abba, Father, all things are possible unto thee; take away this cup from me: nevertheless not what I will, but what thou wilt.
I'm not convinced that Abba translates as "daddy", either. The sense of Jesus' words is, "Yah my father, The Father, all things are possible unto thee ..". "Daddy" just doesn't do the moment justice.
The narrative of scripture, the OT and the Gospels, chronicles the life of a son, the nation of Israel, who did not want the kind of relationship that Jesus had with his Father. However, the love of the Father must have expression, which is why it then came to the Gentiles. Paul writes:
For ye have not received the spirit of bondage again to fear1; but ye have received the Spirit of adoption, whereby we cry, Abba, Father.
-- Romans 8:15 (KJV)
There is little room for doubt that the word "Abba" reflects a more intimate relationship between a son and his father.
1. Hebrews 12:18-24