I was looking at Ancient Greek history and found out about Linear B. It was a deciphered syllabic script that was used around 1000 BC. But, there was a system called Linear A that was used from 1800 to 1250 BC. The Rigveda was written around 1500 BC. This means that, unless texts of Proto Indo-European itself were found or something older than this (prob. Anatolian), if the hypothesis that these are Indo-European languages is true, this could be right.
Potentially, but probably not.
It's true that the oldest Linear A inscriptions (c 1850 BCE) are older than the oldest cuneiform Hittite inscriptions (c 1750 BCE).
However, many linguists over the years have tried to link the "Linear A language" to Indo-European, and none have been particularly successful. Hittite, Luwian, and the "Linear B language" (Mycenaean Greek) all have lots of very distinctive Indo-European word roots and morphological patterns, which the "Linear A language" doesn't. And the null hypothesis, in the absence of any real evidence to the contrary, is that there's no relationship.
Moreover, if we're getting into edge cases, some "Luwian" inscriptions are even older. The hieroglyphic Luwian writing system didn't really come into its own until the 1400s BCE or so, at which point it definitely encodes actual language. But there are some very early "proto-hieroglyphic" markings from centuries earlier. It's unclear if they actually encode language or not (most likely they're more along the lines of "this picture is the royal seal for this king"), but it's technically possible that they do.
So, the Anittas text (c 1750 BCE) is generally taken as the oldest definite Indo-European writing; it's definitely the oldest one that linguists can agree on.
I think the oldest indo-European recorded text is Anitta text, with theoldest fragment VAT 7479, a.k.a. CTH1A dating from the 16th or 17th century BCE, much older than Linear B. Furthermore, it is a real text, and not accounting documents like Linear B tablets.
That said, to answer your question, we know very little about the language of Linear A (and Cretan Hieroglyphics). Given the similarities between Linear A and B, we think we know how linear B was pronounced, and beyond that, almost nothing is known. Argument to link it to various language families — both Indo-European (Greek, Anatolian, Indo-Iranian, a “new” unknown branch) and non-Indo-European (Semitic, Tyrrhenian) — have been proposed, so we really have no idea (or too many contradicting ideas, which is essentially the same).
So you’re free to speculate what you want, but barring significant progress in decipherment — which likely would need significant archeological discoveries to increase the amount of text we have: currently the total corpus easily fits on 2 (A4/Letter) pages. And no matter whether the language is Indo-European or not, any progress in the decipherment will be interesting.
Never say never, but the odds Linear A recording an Indo-European language do not look good. First of all, assuming that the phonetic values of the symbols correspond those of Linear B, it is not possible to make any sense of the texts. It looks like the language of Linear A had a high number of affixes and that's not something you expect from an Indo-European language, at least the ones we know of.
Nevertheless, if at some point and against all odds it is proven to be IE, the Linear A texts would qualify as the oldest IE texts available to us. They might not qualify though as the earliest attestations of IE words, as in Assyrian cuneiform tablets from Anatolia we find personal names belonging to speakers of Anatolian languages. You would then need to decipher Cretan hieroglyphics as IE in order to go back to the 3rd millenium BCE.
At this point, it is a fact, or at least overwhelmingly probable, from Miguel Valerio's paper(https://www.academia.edu/218699/2007_-_Diktaian_Master_A_Minoan_Predecessor_of_Diktaian_Zeus_in_Linear_A) that at least some words in Linear A are of Indo-European origin such as "Du-pu-re" for double-axe, which is clearly related to the Indo-Iranian 'tapar.' 'Pi-Ta-Ja' possibly is a rendering of the number 5. There is also some, more speculative, evidence of gender distinction. Garuth Alun Owens has made an extremely good case for an overall Indo-European origin. The Egyptian incantation rendering some of the Minoan language looks like it has at least a few Indo-European words. Hubert LaMarle made a very inconsistent case, but some of his points are good. Overall, it is more probable than not that Linear A is recording an Indo-European language, although it could have been used to record other languages as well.