Yes, you can. It’s not difficult in the current economic environment to build an AR for under $400.
The question I would advise you ask yourself - why would you want a $400 AR?
I made a living building AR’s for a while, and still build a dozen or so for others each year. I’ve seen a large number of folks very excited up front to build an AR, especially a low budget Mil-spec carbine, since that’s the advice so many fools regurgitate online, then quickly realize the novelty of a $400 noisemaker wears off pretty quickly. So I’d get the same folks back 6mos to a year later asking 1 of 3 questions: I don’t shoot this thing any more, 1) can you spend more of my money to make it more useful, 2) can you spend more of my money to build an upper or rifle which is more useful, and/or 3) can you help me sell this because I never use it? (Or would you buy this from me?) As a person with at least some sense of moral character, I advise everyone who asks about a cheap carbine to really think about how much use they’ll have for it, and how much fun they’ll really have burning money in the form of cheap ammo and loud noises. Some folks love it, but most folks find they want more from their rifle. Whether smaller groups, longer range, hunting capability, action competition capability, what have you. The 16” Mil-spec carbine is far and away the most popular option on the market, but in my experience, it’s the least suited for any given purpose. But hey, you can build one for about $250 if you dig hard enough.