because "not" is an adverb, meaning you can only use it to modify verbs and adjectives. Since "problem" is a noun, you should use "no" which is an adjective.

You can say not a problem or no problem. BTW, this is often used instead of saying Thanks.

No problem is short for ... it is no problem. We often say not a problem in place of you’re welcome.

I think "no "problem is better. Because "No" problem is discribing "I don't have any problems". On the other , "Not problem "is describing "It is not a problem." ,😀