Constant growth DCF models

I came across a question where the FCFF at the beginning of t=1 is given, and said cash flow is expected to grow at a constant rate. My approach to computing intrinsic value was to grow the cash flow one period to t=2, and then discount it at WACC - g to get a terminal value at t=1. I then discounted back the terminal value, and the given free cash flow SEPERATELY for one period, at the WACC, and then added them to get the intrinsic value at t=0. Even though my answer is correct, I noticed that the solution directly discounts the given FCFF(t=1) at WACC - g to get the firm value. I’m a bit confused about this approach because I always thought that the constant growth model can be directly applied only if the cash flow at t=0 is growing at a constant rate. Could anyone clarify this?

(PS : If my question is too confusing to understand, I don’t mind restating it with some actual numbers)

When you mean beginning of t = 1, you mean t = 0, it would be today. The constant growth model can be applied to whatever cash flows and whenever as long as they grow at a constant rate. If the numerator (in the constant growth model) is a cash flow that is for some period other than t = 1 (end of period 1), then just make sure to discount it to today.

Sorry, my bad. I meant end of t=1, so not today, but a year from now. So, can I apply the model even if the constant growth period begins at the end of t=1, as opposed to t=0, without having to discount the calculated amount back a period?