Can I use T-Statistic for constructing a Confidence Interval for sample from large population?

Can I use a T-Statistic to construct a Confidence Interval for a sample collected from a large population and without knowledge about the population's standard deviation? I know the "model" answer is that a sample, even if the sample size $n$ is small, would have to use a Normal Z statistics if it was collected from a large population. But I have used a T-Statistic in a problem like this one because earlier, I felt that it would be more appropriate to use a T-Statistic since I'm having the standard mean error estimated by the sample standard deviation. And now, I am worried that I've done wrong.

So, can I use a T-Statistic to construct a Confidence Interval for a sample collected from a large population and without knowledge about the population's standard deviation? In my case, $n=8$. If no, why would it be wrong to use a T-Statistic in this case? If yes, also, what are the reasons for being correct to use?

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