If you want to test a mean difference withot making parmtric assmptions about the distritribution, then you will have to bootstrap the distribution of the t-statistic. This would be the "non-prametric alternative" to the t-test.

Some may tell you that the signed-rank test (Wilcoxon test) would be the alternative - but that would test different hypothesis. So this is somethig different and not really an alternative.

You certainly can do a t-test for 6 samples. The t-test is designed for small samples. The important point is that the assumption (here: the differences are approximately normal distributed) makes sense. With small samples, there is no chance to demonstrate that this assumption makes sense just by looking at the data. You need some understanding of your data (the variable, how the values are produced, what the variable means) to judge your assumptions.

To test for paired difference Wilcoxon signed-rank test is a recommended nonparametric test. It is used to determine whether two dependent samples selected from populations have the same distribution.

Jochen Wilhelm Kamoru A. Adedokun Thank you so much for your answers!