So how do we know that the translation we are reading and understanding is correct.
We don't. A translation depends on the translator's own understanding of the text and what meaning they see the Sanskrit words, which have multiple, as having. For example, 'go', "cow", also means "ray of light" or "heaven".
Even in those rare cases of translators understanding the mantras, we do not get the whole understanding in just the translation but the explanation and commentary. There is always an explanation to the mantras to make sense of them and unpack any seeming contradictions.
Whether a commentary is provided for us or we understand the context ourselves, it is necessary to have the context surrounding a mantra so we understand its meaning and what it is referring to.
And that's how people have understood the Vedas when they were first composed.
How people understood the Vedas when they were first composed was through their understanding of Vedic Sanskrit, the figurative use of language. As others have said, the Nirukta demonstrates this. Sanskrit words could be derived from a root which give an idea of its etymological meaning and therefore the meaning of the word. This understanding is lost when people take a word as meaning one thing without knowing its etymology. So, the word could be translated literally, but its use in the mantra could be in the context of its etymology. This context is lost without knowledge of Nirukta or Vedic etymology. This use of language continues in subsequent texts and is why there are misinterpretations - because people overlook the fact that many of the words are translated as meaning one thing when they have multiple meanings. There is a lot of wordplay and double-meanings which most people do not see.
I'll give an example. The word 'Puruṣa' is translated as either "Self", "person" or "man". It is said to come from the root 'pṝ'- "to fill". Just from this, we do not see how it can mean these three things. We are missing the context. However, Nirukta adds,
2.3. Puruṣa: puri ṣāda ("one who sits in a city"); or puri śaya ("one who sleeps in a city"); or is derived from ‘pṝ’ (“to fill”), i. e. he fills the interior, with reference to the inner Self.
We find this understanding in the Upaniṣads, as well as other etymological meanings. Bṛhadāraṇyaka Upaniṣad:
1.4.1. Since, before (pūrva) all this, he burnt up (us) all the evils from everything, he is puruṣa.
2.5.18. This Self (puruṣa) is lying-in-the-citadel (puriśaya) in all citadels. There is nothing that is not covered by him, nothing that is not surrounded by him.
So, this contextual understanding informs all references to puruṣa in the Vedas, Upaniṣads, and subsequent texts. And this is just one word; it is the same for many other words. This means that, from 'puruṣa', it is wrong to deduce it only means 'man' or 'person', which some translators do.
Further, its place in Yoga or Sāṃkhya is taken as being different to ātman but, from its etymological meanings and context in which it is used in texts, we see it is no different. In the Vedas, puruṣa was used in the same way Brahman was in the Upaniṣads and Vedānta in general.
Aside from all of this, we won't get the full understanding just from a translation, no matter how good it is. The Vedas' mantras deal with experience or knowledge of the Self, just like the Upaniṣads do. The difference is in how they went about it. The Vedas used a lot of analogies to convey their teachings but in a way where we don't see the comparison. E.g., two birds on a tree with one eating fruit whilst the other looks on. It is a metaphor but, from just this image alone, without experience or knowledge of the Self, we do not see how it equates. Several Upaniṣads then used the same imagery to clarify how it relates to the Self, the same way they did with the imagery of the chariot, charioteer, reins and horses.
The mantras are also emotive in nature. In other words, the language and imagery is inspired by a feeling that is being expressed. This is the same as how poets express emotions not in a literal manner.
So, we miss all of this context from just reading a translation. The purpose of the mantras is to digest the imagery and still the mind, where the meaning becomes clear. Another angle of the mantras is that, often, what the mantra is saying is the same as the effect on the mind the mantra has. They are both instructions for how to practise it and what effect it has. Simplified, like with any mantra, its power is in its vibration and effect on the mind more so than it is a literal meaning of the words which comprise it. The meaning of the words and the mantra is revealed (śruti) in its transformative and quietening effect on the mind it has. It is from this place of stillness and seeing the meaning of the mantras that each Vedic mantra was inspired by, created from and pointing back to.