It is hard to answer with 100% confidence. The text does not specify it explicitly.
However, I would guess, Marina saw her Grandmother before, maybe for some short period of time. The key word here is "близко": "Если бы я не поехала, я не узнала бы близко свою бабушку."
I would not say it like that if I had never seen her at all. It would not make sense to specify "близко" in that case. So, as I understand this phrase, she knew her before, but not "близко" (not so closely), maybe she just met her once or a few times before.
If to suppose she had never seen her grandmother, I would say: "Если бы я не поехала, я так и не увидела бы свою бабушку.". The "так и" part is to emphasize the failure to get a result, it can be omitted.