Finding an agent is harder than finding a needle in a haystack. But most major publishers, and even most mid-range publishing houses, will not look at manuscripts submitted directly to them by authors. Miraculously, there are some exceptions. Apart from DAW, these tend to be small houses. However, in matters of publishing, size doesn't always matter. Chicken Soup for the Soul was published by a small publishing house.
In all of these cases, be prepared to wait three to six months for a response. Make sure you follow their submission guidelines to the letter. If you don't, they will toss your manuscript into the recycling bin without a second thought. Whenever there is stiff competition, remember: Do not give anybody an excuse to throw your submission out.