Having Problem about DownConversion

I hope, you are doing well. I want to ask question about baseband conversion.

Background:

• I generated two AM signals in MATLAB, which one of them is shifted in time.
• I multiply the signals with $cos(2pi f_c t)$ in order to obtain IF signal.
• I filtered the IF signals with $f_c$ cut-off frequency.

In this way, I aim to downconverted to signal to baseband.

My problem is, when I try to cross-correlated the baseband signals, my result peaks at zero.

I expect to see the delay, but I could not. Am I missing something?

Notes:
I am exact sure, my cross-correlation function works perfectly. I tried this function before baseband process.
Also, in order to obtain both I and Q components, I try to multiply my signals with sin(2pifc*t). Nothing changes.
MessageSignal: Audio Signal.