It's funny how I always feel unqualified to answer these questions, because I seem to fall outside the range of most common experiences. But since I'm only in the sixth week of HRT, I'll still give my personal response.
As with most things, I think everybody's experience is unique. That said, I suspect few will say that they felt an immediate reaction other than the euphoria of finally starting down the path where they belong. And that is a significant and powerful part of the journey.
Since I began at half of the low-dose protocol for estradiol and a quarter of the LDP for spironolactone, I can easily say that I've felt no chemical effects yet - which is exactly what we want. My body is absurdly sensitive to all kinds of things, including medications, so we wanted to be sure that I didn't experience any negative effects (too-low blood pressure, allergic reactions, etc.) If all goes well, I'll finally reach the low dosage next month.
So, I'm the wrong person to ask, but this has been my experience so far. Given my super-gradual approach, I suspect the onset to be nearly imperceptible.