No, but you can set another automation that runs the first time you ask for the lights to be switched on each day that triggers on the lights going on and action is to push the brightness to full.
Quickest way (without knowing the rest of your config) would be to set an input_boolean to on with your automation above, and then use that as a condition for the new automation, and switch the boolean back off in the action of itself.
I think he is saying that the input_boolean would just act as a flag that says “hey, this light was turned off using your transition”. So you’d turn that on in your script above. Then create another automation that fires when the light turns on. The new automation would use your boolean as a condition. If the input_boolean is on, make the light 255. Then turn off the boolean in the same new automation.
Or you could probably simplify it even more by creating an automation that always makes the light 255 when it turns on. You’d just never be able to turn it on at a different brightness. You would have to turn it on and then dim it after.