TBH in the early weeks of pregnancy, just drink what you can, and just drink to your thirst. I personally wouldn't force anything down that could very well bounce back up! If you're worried about hydration, you could sip on a sports drink, I know it's recommended if you have really bad morning sickness.

I struggle with 2L of water when I'm not pg..let alone when suffering m/s in the first trimester. I've never measured how much I drink when pg or breastfeeding, I just drink if I'm thirsty.

Another suggestion could be to drink your water as some kind of tea.. like peppermint or ginger.. that can help with nausea too.

Hope that helps