I will argue, we do not.
We do not have anty Galilean Aramaic transliterations.
We have Koine with a few spread out transliterations as would be expected from a collection of Galilean parables.
We do not have any gospels that show Aramaic primacy, as one would expect had any information came from the real Galileans.
Take into account the gospels all portray the Galilean apostles as cowards who ratted on their buddy, and denied him, and who fled with their tales between their legs after the crucifixion.
It is also scholars general opinion the 12 are fiction, and that we probably had 3-4 real Galilean apostles, his inner circle.
Everything we have are attributed to, but cannot be susbstantiated to any Galilean.