# Confidence interval from a non-probability sample?

From what I understand, to generate a margin of error to have confidence intervals for a given estimate one needs the standard error of the estimate (SE). For the SE one needs information about the sample size. Is it the fact that the sample size is non-existent when doing say, purposive or quota sampling, what impedes us from generating sampling errors of the estimate to later calculate confidence intervals?

I then thought, well, regardless of the sampling method use (probability based or not), you'll end up with a certain sample size. Can this not be used to then calculate SE of the estimate, and ultimately confidence intervals. Or perhaps, it all comes down to my final suspicion: one can certainly calculate SE for an estimate and then proceed to generate the CIs, but these will ultimately be wrong given the poor consideration of the sampling design.