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If I'm not told that they're non carriers, and if I don't have proof of their geneotype based off of progeny, when can I assume they're non carriers for a trait?

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All the time.

Unless you are specifically told/shown they are carriers, they are assumed to be Wild Type and do not carry the mutation.

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You can only rely on statistics in this case. Check the population the person is coming from for statistical probability to be carriers.

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Usually you assume neither situation. You are given some probability that they carry the trait based on measured allele frequency in the population. Then you use that probability in any downstream application, such as calculating the probability the children are carriers or affected with the genetic condition.

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