Most people cannot. The qualifying cutoffs are there to limit entries to a number that the course can handle. You certainly don't have to be elite, but you do need to be better than average by a fair bit.
Your best bet is to work your way up to a local marathon. Find a training plan for a 5k. Train and race a couple of those, then move on to a couple of 10k's. Then set a little longer goal of a half marathon. Then stick to a training plan for a full marathon. Pick one that's fairly close to you and fairly flat. Local will mean you don't have to worry about traveling to it, and flat will make it easier to pace yourself.
Once you've been through one marathon, you'll have a much better idea of what it is all about - what the training is like, what the race is like, how much you would need to improve to qualify for Boston, and how long that might take.