Frequency change detection in step-wise frequency chirp
I suggest monitoring the phase versus time directly instead of frequency. Frequency is the derivative of phase so the slope of the phase would indicate the frequency. Detrend the phase slope for the starting frequency and then the point in time where the phase starts to ramp up should be easier to detect. The window in which to detect this change will be balanced with the SNR of the signal itself.

Since frequency is the derivative of phase, it will be more sensitive to high frequency noise (the derivative is a high pass function), which is why monitoring phase directly could be a more reliable approach.