This question is big and open-ended. Transition is linked to the growth of small instabilities in the flow field, but the link is not straightforward. The physics involved include the external flow field, the pressure gradient and of course the geometry of the solid surface (if present) adjacent to the flow field. In a simple analysis, the region that interests you is confined between the points of instability and transition. That distance delineates the spatial region while the temporal factor can be determined by the timing (speed) of the external or main flow field. If you are interested in the details, I recommend you consult Chapter 17, "Origin of Turbulence II" in Boundary Layer Theory, 7th. Ed., the classic text by Hermann Schlichting. I would suggest starting with Section b. "Determination of the point of instability for a prescribed body shape." There are a number of figures containing data that can help elucidate the extent of the transition region based upon certain assumptions regarding your geometry and flow field. This section will also refer you to other sections of the text for related information. You will not find a concise answer for your question, but this reference will provide a lot of relevant insight for you. Unfortunately, time will be required to go through and process the knowledge contained within.

Have a look also to this well knonw textbook (Chap. 5)

https://www.cambridge.org/core/books/introduction-to-hydrodynamic-stability/52F918FA38D2984D4638F2D04C8CFA3A

Hi, in my opinion an important fact it related to open flow or flow inside walls. Normally when you are considering flow inside walls the transition is just a function of the mean velocity, density, sizez and roughness. But the external influence to the system decide when the transition occur. In special conditions, you can have laminar regime inside pipes, for example, for Reynolds higher than 10000. In open flow the transition is related to the length of flow over the surface. really the subject is extensive and many books consider this phenomenon in details.