There are a number of ways to ensure the validity of one's scale: Content, discriminant and convergent validity being just a few examples. Whether I would call them "advanced" I do not know.
Construct validity can be tested and achieved by means of CFA which is a well-established procedure. Why do you explude CFA on purpose?
In the following paper, I try to follow rigorous procedures for scale validation, which can be acceptable in most top journals. Hope this is helpful.
Kim, T.-Y., David, E., Chen, T., & Liang, Y. (2022). Authenticity or self-enhancement? Effects of self-presentation and authentic leadership on trust and performance. Journal of Management. https://doi.org/10.1177/01492063211063807.