What you are describing sounds like a pilot study. The resource linked below gives this advice re pilot studies: "Pilot studies should not be used to test hypotheses about the effects of an intervention."

• https://www.nccih.nih.gov/grants/pilot-studies-common-uses-and-misuses

That resource addresses pilot studies prior to RCTs primarily. But the advice is just as applicable to your situation, IMO.

I hope this helps.

With such a small sample size (12 per group), a linear mixed model can be used. Yet, it may face limitations in accurately estimating effects and variance components. The statistical power may be low, especially if the expected effect size is small, so a power analysis or simulation could clarify feasibility. Simplifying the model structure by limiting random effects may help prevent overfitting. Alternatives like generalized estimating equations may also be considered if the primary interest is in fixed effects. Finally, using restricted maximum likelihood estimation and checking assumptions carefully can improve robustness in small-sample contexts.

Thank you so much all for your answers

Linear model will work for this sample size though relatively small. But the desired accuracy of the results may not be obtained.

For obtaining more accuracy, sample size is to be larger.

Note that sample size which is greater than 30 is usually treated as large sample.

Accordingly, the results will be of reasonable accuracy if sample size is more than 30.