you can say "mam czas po obiedzie" - which means you have time after "obiad"- so late afternoon/early evening.

Accusative is "czas", Genitive is "czasu".

"mieć" takes Accusative, but when a verb needing Accusative is negated, then it takes Genitive.

Alternatively, you may have seen something like "Mam trochę czasu" (I have some time), "trochę" and other quantifiers like that need Genitive.

... could it be that you are asking about a negative so "nie mam" would take "czasu" as opposed to "mam czas".....

It's a perfectly fine sentence, but nothing here guarantees that we're talking about dziś = today. Maybe we're discussing next Saturday.