You can just buy a translation of the Septuagint, or even read one online. No biggie.
I recommend
A New English Translation of the Septuagint (aka NETS).
The Masoretic text isn’t the only Hebrew Bible text that ever existed. It’s the reading that was agreed upon and collated later, long after Jesus’ time. So it would have been impossible for Him to use the Masoretic text exclusively, except by using His divine omniscience.
It’s true though that the
ancestor of the Masoretic text had already existed during the time of Jesus, known as the ‘proto-Masoretic’ and the ‘proto-rabbinic’ text.
(Strictly speaking, the ‘Masoretic text’ refers to the Hebrew text which has vowel markings or
niqqud (remember that Hebrew was originally - and still is, to an extent - is an abjad, a writing system that only represented consonants) and concise marginal notes, added to the text. These ‘additions’, which was fixed from the 6th to the 10th centuries, are collectively known as
masorah (the “transmission” of a tradition), and the Rabbis who developed these are known as the Masoretes. When we identify a text as ‘proto-Masoretic’ it really means that text is nearly identical to the consonantal text - i.e. the letters only, without the vowels or the marginalia - found in the MT and which could well be the ancestor of the MT’s consonantal text.)
You’re right that “the Masoretic text isn’t the only Hebrew Bible text that ever existed.” The thing is, as the manuscripts from the Judaean desert (Qumran specifically) imply, there was a multiplicity of versions. The proto-Masoretic text
was (going by the numbers) the most-represented form of the text in the manuscripts so we can assume that it was the most-commonly used version in the Holy Land before and during Jesus’ day, but we also have (fewer) texts which represent the Hebrew version underlying the Greek Septuagint
and a Hebrew version which is quite similar to the later Samaritan version of the Torah/Pentateuch.
But here’s the thing. By the time we get to the later 1st-2nd century (from other sites in the Judaean desert we know was inhabited by the 2nd century), we only have proto-Masoretic manuscripts. So we might assume that that particular version was singled out as the ‘standard’ by that time to the exclusion of the other versions. But it’s not like whoever chose it picked a version at random; they chose what was by then the most common text, at least in Palestine.