Standardized working hours and actual working hours

Dear All:
For a general production function, we always have Y_t=A_t K_t^{\alpha} L_t^{1-\alpha}. I know that i can not directly get the K_t data from Fred or any other source. So, I constructed a K_t by using law of motion and initial starting quarter. But i have an issue regarding to the L_t, which is usually standardized and between 0 and 1. In my case, it is 0.3 (steady-state).
If I need to know the exact time value of the 0.3, for example, 30 hours a week or something like that, can I just take the average of weekly working hours data from the Fred and make it equal to 0.3, so that i can get the exact weekly hourly value of standardized L=1. am i doing correct?.
Thanks your help.

What are you trying to do? The model features constant returns to scale, so L_t can be arbitrarily scaled.

I want to extract total productivity shock A_t from the production function. This is constant returns to scale production function.

The scale of A_t will also not be well-defined, only its percentage fluctuation around the arbitrary normalization. So if you normalize hours or use average weekly hours does not matter.