Need advice: getting too full before getting the amount of protein I want to get

I've been a vegan for a couple months now, but I've only been working out for about a week now.

However, despite myself planning my meals, I have been feeling like I'm either not planning them correctly, or my body just doesn't want to fit all of the food I want to eat. My goal right now is to get to between 150 to 160 lbs, and I've heard time and again that I should aim close to my target goal in order to get the gains I want.

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Now, I'm still new to fitness terminologies, so I could be wrong about the amount of protein I actually need (since I've seen tons of answers on the subject). I am currently doing the Phrak's Greyskull LP Variant program as recommended from the fitness reddit. While I am looking to become more fit and reach a more healthier weight than I currently have, I'm aiming also for some aesthetic muscles versus gaining strength. I'm sure they probably go hand-to-hand, but just to further clarify my goals. I understand too that I won't see that straight away until I start losing weight, of course. So to do this, I feel like I have a good start, but I seen to get around 70g every day before I'm just not hungry until the next morning. I've been eating beans, oatmeal, putting protein powder in my meals. I will admit I haven't tried smoothies or shakes yet, so that could be the obvious answer. But having said that, would that mean I would have to use tons of protein powder to get the amount of protein I'm shooting for, or do I not need as much as 150g every day? I don't mind having protein powder, I'm just looking for any advice for my main issue; getting too full before I can get enough, even with myself eating protein-packed foods. Maybe some others here have that issue.