A quick rundown of LXX Septuagint "evidence":
Here are all actual evidence we have of the Septuagint, in a neat timeline:
Aristobulus, assumed to be a high priest, but actually a Jewish Greek philosopher 110 BC
Philo of Alexandria 50 AD inspired by Aristobolus only says 5 books were translated
Josephus 93AD recounts the translation by Philo's words
Origen 250 AD
Eusebius 260AD apparently quotes Aristobulus, but only mentions that only 5 first books of the Bible was translated to Greek
Oldest copies we have of Letter of Aristeas in its modern form 11th-15th century AD name drops Aristobolus, and it is not clear that it mentions only 5 books, but it is a known forgery and hoax as it messes up historical events.
So what we see is while the Septuagint does not exist, the first five books of Moses probably were.