@drummachine Your bodyweight is relatively low already - I'm not suggesting it's unhealthy (and you may have lighter bones than I do), but we're the same height and there's a big difference in our weight!
Which is to say, save the cutting for when you've put on a good amount of muscle mass and you're edging towards the higher end of a healthy BMI. Right now, there probably isn't much to cut (in terms of excess fat) and there may not be that much to reveal (in terms of muscle underneath). That might not sound good, but it's actually a great place to start
By adding more lean mass, you'll automatically get more muscle definition. In fact, depending on how your training and gaining goes (and your goal physique), you may not ever need to cut.
As for the daily protein intake, ouch!
Great work in buying some protein-rich whole foods, but I second the recommendation to get some protein powder and protein snacks - it will make everything so much easier.
Either way, it sounds like you don't eat a lot on a daily basis? (I'm making assumptions here, based on the 10g and 40g figures you mention.)
Adding muscle requires lots of energy, in addition to extra protein, so don't be afraid to eat more than you normally would (on both training days and rest days). This can feel uncomfortable initially, so start slowly and gradually increase your portion sizes over time
