A/C takes longer to blow cold air

My A/C has been working great since I bought it new. Last month I noticed that it was taking much longer to blow cold air. In the past, I could feel cold air within a minute. Now it takes 5 or more minutes before it starts to blow cold air. But once it starts, it gets super cold like always. I often switch the inside air circulation off until the cabin temp gets lower.
I've cleaned the coils and the freon is fine. I'm not an experienced mechanic but for a 20 year old girl, I can do all my own maintenance and most all minor to moderate car repairs. Here is what I've observed. This only happens when I start the car after the engine has completely cooled down. If it's warmed up, the A/C blows cold right away. For the past few mornings, I've raised the hood to see if I noticed anything since it only malfunctions when the engine is cold. It seems the A/C doesn't blow cold until the electric fans kick on for the coolant system. Could there be a correlation between these two? If not, what would you suggest?
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Comments
That's a technical tern, by the way.
But, to be sure, you would first need to have the A/C charge checked. It is possible that over time, freon has leaked out a little (they do that).
If the pressures are low on the A/C, then it could need to be charged.
And please don't buy those DIY kits, they can do as much harm as help.