Probably the best way to figure out the sample size requirements for a CFA is by using a Monte Carlo simulation. A simulation allows you to consider your exact model (i.e., the precise factor structure and expected parameter estimates) and to simulate realistic conditions (e.g., missing data, non-normal data, different estimators) instead of relying on rules of thumb that may not apply to your specific scenario. Simulations allow you to examine potential parameter estimate bias, standard error bias, statistical power, accuracy of fit statistics, and more.

See:

Muthén, L. K., & Muthén, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 9(4), 599-620.

Christian Geiser Monte Carlo simulation is a pretty high standard for a simple CFA. Since the standard of 10 participants per coefficient (sometimes as low as 5) is so widely used, I would recommend relying on that in writing up the results. Then, if the reviewers demand more justification than that, options like Monte Carlo would be appropriate.

Prof. Christian Geiser and Prof. David L. Morgan, thank you for your responses. If a relationship were to be established between Monte Carlo simulation results and fit index values, wouldn't the values influenced by the sample already be low? In this context, if the fit index values are good, I would like to argue that the scale is validated with at least five times the number of participants as the number of items... Of course, the opinions of the reviewers will be important.

Addressing the issue of numbers to run CFA, in general, there is some agreement on large samples in scale development. Larger sample sizes are likely to result in more stable correlations among variables and will result in greater replicability of EFA outcomes (Worthington & Whittaker, 2006).

The link below spells out detailed procedures on how to go about EFA, CFA as it also looks at the different views on sample size parameters. Other issues are also discussed on the factorability of the scale etc. p. 8ff. https://www.researchgate.net/publication/361400957_Advancing_Psychometrics_in_Uganda's_Institutions_of_Higher_Learning_with_Emphasis_on_Structural_Equation_Modeling_SEM

Ali Ibrahim Can Gözüm If you only have 5 participants per parameter, then there is nothing further you can do at this point. As you say, the outcome will be up to the reviewers.