Before you do any sheet metal work, I'd try removing the front hinge bolt, and install a couple washers under it, where it's pushed in. Try to raise it up to stock height. By doing that, it should lower the rear of the hinge ...where the pivot is (it's like a lever). I don't know if it'll give you enough 'lowering' effect to make up for your gap, but it might. The rear of the hinge where it bolts to the body may have an up/down adjustment too. Or, the holes could be elongated to increase travel if necessary.
If not, you can 'try' to pull out the hood area where the hinge mounts (as suggested by others). The bent in region. That's beyond the capabilities of most people. It wouldn't hurt to get a paintless dent guy to put his eyes on it and see what he thinks. Generally they 'pry' and there's not much to pry onto. But worth a call though just to see.But
At a body shop, if I were working on it, and had the hood off, laying upside down on padded saw horses, I'd grind the paint away (around the bent hinge mount area), tack weld on a couple metal plates and using pry bars gently lift the area back up to stock height (to match the other side). Then remove the plates, prime and re-paint. Should be able to make a nearly invisible repair. I worked at a body shop for years. That's how I'd deal with it. But try to adjust it out ..or a paintless dent guy first.
The front hood/grille doesn't line up very well either, has this been in a wreck? Panel alignment is a tricky issue. In a crash repair situation, a lot of shops want to move cars through pretty quick and get on to the next one. Truthfully, most customers don't notice panel fitment issues like that ...till later on -- and they don't usually come back to the shop. If they do, the shop would try to resolve it. Poor panel fitment is the mark of sloppy work. It takes a long time (sometimes hours) to get panels to line up nearly perfectly. That means lost profit for shops. Either way, you should be able to get the hood to fit properly given enough effort and time.
