I think explaining the central limit theorem needs two elements: the sample size and the number of samples drawn.
But nobody seems to talk about the number of samples drawn when they are making some infererence $\mu$ using the central limit theorem and only mention the sample size, $N$ and its distribution, which means they only use one sample group to infer population $\mu$.
I thought, however, there should be lots of samples each of at least 30 elements, and accordingly, lots of sample "means", and their distribution, not just the distribution of one sample group.
Please kindly help me to correctly understand the Central Limit Theorem and inferring the population mean, $\mu$.