This depends on your research question. I can think of different reasons why to start with one over the other. For example, if it is a novel area of investigation and you are unsure what types of variables to measure quantitatively, you can use qualitative methods to gather preliminary data to inform the use or development of psychometric instruments. On the other hand, you could begin with quantitative research to investigate the relationship between different variables and then use qualitative research to add depth and perspective as to why these associations exist. These are simply two examples but you need to deeply consider your research question and how a mixed methods research protocol would help address this.

Dear Jérémie Richard this is very clear explanation and makes things much simpler, thank you very much

Just to add to Jérémie Richard's answer, beginning with a smaller qualitative study to develop a larger quantitative study is known as an exploratory sequential design (qual --> QUAN), while using a smaller qualitative study to follow up on quantitative results is known as an explanatory sequential design (QUAN --> qual).

The best knows textbook on mixed methods is undoubtedly Creswell and Plano-Clark, 2017 (3rd edition).

Dear Prof David L Morgan thank you very much sir! I will refer the text

Ordering quantitative and qualitative approaches, or using the two approaches simultaneously, in mixed methods research (MMR) depends on one’s intent to blend the two data sets. If you intend to use the quantitative outcomes to shape the follow-up qualitative data collection that clarifies the significance or insignificance of statistical findings, you should start with the quantitative approach as a first independent stage, i.e., collect data through a quantitative tool (e.g., questionnaire) and analyze it statistically first—this is known as explanatory sequential MMR design. In case you aim to use the qualitative data to construct quantitative materials and carry out a follow-up quantitative stage of data collection, you should begin with the qualitative approach as a first independent stage—this is known as exploratory sequential MMR design. In convergent MMR design, the two approaches are used concurrently at the level of data collection and analysis if the intent is to converge the two data sets. You could check out the textbooks by Creswell and Plano Clark (2018) and Tashakkori et al. (2021) for relevant insights. Here are the full citations.

Creswell, J. W., & Plano Clark, V. L. (2018). Designing and conducting mixed methods research (3rd ed.). SAGE. https://us.sagepub.com/en-us/nam/designing-and-conducting-mixed-methods-research/book241842

Tashakkori, A., Johnson, R. B., & Teddlie, C. (2021). Foundations of mixed methods research: Integrating quantitative and qualitative approaches in the social and behavioral sciences (2nd ed.). SAGE. https://us.sagepub.com/en-us/nam/foundations-of-mixed-methods-research/book252072

Good luck,

Dear Isuru Koswatte, I suggest reading the "Integrating Qualitative and Quantitative Methods: A Pragmatic Approach" by David L Morgan.

I found it very informative and useful.

Dear Prof Mohialdeen Alotumi thank you for the very detailed yet clear explanation! I will refer to both texts

Normally, you report in the order you did things.