I do have a suggestion....... And a possible cause.
The fan starts, a precision timer is sometimes included in BETTER air conditoners before the compressor kicks in in order to prevent "hot starts" where, for example, a power "flicker" shuts it down and it tries to re-start before the pressure has bled off.
Due to the air moving about the t-stat now senses "Cool enough" and shuts down.
Finally it's hot enough even with the fan running and it continues to operate.
The suggestion:
Many times I hear complaints about A/C Noise.. The solution to that is to run the fan on HIGH, not automatic.
Your brain will very quickly "Filter" the sound of the fan and the blower "noise" which approximates white noise will also mask the kids and dogs on the next site (won't completly block 'em but will mask 'em) so you win, win, win with the blower on high.