My specialty is Chinese, which didn't really have any pronunciation guides until the 19th century, and yet we can still make educated guesses at how words used to be pronounced at different times and in different languages.

Modern Standard Mandarin is a language. Chinese is a group of languages historically spoken in regions ruled by a single government and which currently remain linked by most of a single writing system (Traditional and Simplified haven't yet diverged beyond being different fonts).

This is done through a variety of methods including looking at the poetry written in a given language. It's why "afro" and "although" can rhyme in hiphop but, if Shakespeare had for some reason been talking about Othello's truly magnificent hair, wouldn't have been able to.

If that word or words or language leaked out into the surrounding communities and was picked up by them, we also have more clues. Just because the Chinese didn't have a phonetic script prior to the creation of pinyin, doesn't negate the creation of Wade Giles, the phonetic use of Chinese in written Vietnamese, the use of kanji in Japan, the mind blowing awesomeness that is the Korean alphabet, or the writings of non Chinese travelers to China over the past millenia.

If everyone everywhere is currently pronouncing things with a 我 radical as "e" (哦 鹅 饿 俄), this is a starting point on research which may indicate that the word 我 was once pronounced "e" instead of "wo" (or, more likely, since this is academia, will kickstart a 40 year long argument that no one outside a very specific niche field is even aware exists and which will eventually collect enough evidence to reach a completely different conclusion).

In any case, this is with an extremely documented language that still has a current form. For something like Linear A, absent the discovery of a Rosetta Stone equivalent or three, even if we eventually manage to translate the meanings, we likely will never have an idea of how it was spoken.