Getting published by one of the big five publishers (Hachette, HarperCollins, Macmillan, Penguin Random House and Simon & Schuster) might seem impossible without an agent, but it is not.
Most of these publishers have an imprint that accepts unsolicited submissions or queries. These imprints are sometimes very specific in terms of what genre they publish, others are very broad.
Some are print and many are digital first. Digital first, in most cases, means they publish an eBook version and if it does well, they follow it up with a traditional print run. Not all of them are currently open to submissions at this time, but all have plans to re-open. It is good to bookmark and regularly check back in on one of the websites to see if they have reopened to submissions.
The great thing about being published by one of the big five is they have more design, marketing, and editing expertise than most other publishers open to unsolicited submissions.