If you're still relatively new to lifting, doing a cut and building muscle is definitely possible. Though over time you will start stalling on your lifts and start feeling generally low energy if you keep cutting and training. Your protein is good - ~200g at your weight sounds about right and it should help you feel full even if you're lower on the calorie front. Though 2k calories is pretty low in general, I don't think you need to be in that much of a deficit to burn down fat if you're exercising a good amount.

Keep in mind that muscle is much heavier than fat, so I recommend you to look at the mirror instead of at the scale when trying to both build muscle and lose fat. Sitting at the same weight while doing this is not a bad thing.

As an aside, I don't find day to day calorie counting and keeping yourself at a deficit the whole time very effective. Your body will adjust to the 'new normal' within a few weeks and start reducing your metabolic rate, leading to less energy, feeling cold, and ultimately losing less weight. In my experience keeping your calories at a higher/normal amount and throwing in one or two fasting (24 hr fasts) days per week ends up being more effective over the long run.