No, Czech doesn't use "mít" (to have) this way.
"We are having (=drinking) coffee" translates as:
"Pijeme kávu" - simply "we are drinking coffee"
or "Dáváme si kávu" - literally "we are giving coffee to ourselves"
The sentence here ("Máme kávu") only refers to having/possessing coffee, probably in a box or jar on a shelf.
umm with "ale ne dobrou" the verb is kind of still there, it is the "ne". You could say "kávu máme, ale nemáme dobrou", but in Czech when you are using the same verb in a sentence but only in a negative form, you can just say "ne" instead. For example: "Jsme unavení, nejsme opilí." - "We are tired, we are not drunk." But you can also say both in Czech and English "Jsme unavení, ne opilí." - "We are tired, not drunk."
But I noted a question to myself as to why it is not dobre or dobry etc. I don't see the list of declensions for dobry. If someone can point me that direction please. thank you.
I think maybe endless sleeper answered that partially, saying "dobrou" is accusative while dobra' as I said is nominative.
There are plenty of places where you can look to find the declensions. One possibility is the wiktionary: https://en.wiktionary.org/wiki/dobr%C3%BD
Since "káva" if feminine, you need "dobrá" in the nominative (not "dobrý" - masculine, nor "dobré" - neuter) and then you look up the case you want.
OR you memorize the forms for ONE hard adjective, such as "mladý" (or dobrý) - so far you only need the nominative and the accusative in all three genders. Then you don't have to look up anything, because all other hard adjectives take the very same endings.
Of course I get it, I was just wondering whether it is the same as in Polish where the general rule is to write "nie" (=ne) in one word with the adjectives, but in this very sentence one should write these two separately as well as in the Czech sentence. Two situations. 1) You are telling someone how to get somewhere and say: "When you see a big white house - turn right". And then that person calls you and says "Vidím bílý, ale NE velký dům" /teda vidím dům, který není nějak speciálně obrovský, ale na druhé straně neznamená to, že je 'nevelký', protože stejně dobře může být střední/. 2) You are telling someone how to get somewhere and say: "When you see a white house - turn right. The house is not big but you can't miss it". Then you should say/write 'NEvelký', shouldn't you? I was confused with the audio here because there is almost no pause between 'ne' and 'dobrou' so I thought it was more like: "We have coffee, but not good / tasty".
There is a glottal stop between ne and dobrou in the pronunciation.
I do not think you need to use nevelký in 2). I would not do that.
It is NOT about writing "ne" together with adjectives. It is about using "(is not) big" or "is (not big)". It depends on which part of the sentence is negated. If you create a negative adjectives, it does have the ne- prefix.
The word nevelký is here https://cs.wiktionary.org/wiki/nevelk%C3%BD Note that many other adjectives do not have a frequently established negatives like nedobrý or nevelký, but you can probably create them ad-hoc
"je nevelký" means that it is small
"není velký" means it is not big, but it can still be average size