Publishers are much more likely to look favourably on submissions from an agent, that direct ditto.
How many agents have you tried? One way to choose possible ones, is to look at the thanks from the author to agent/publisher at the beginning of the sort of book you have written.
I tried 6 before one took me on, and after much rewriting, before she thought it 100% ready to send out, that novel went on to attract a bidding war.
I was successfully published for some years, but I’m not writing any more - ideas simply dried up. Which would mean (some would say) that I was never a ‘proper’ writer in the first place!
Needless to say, your covering letter or email should be brief, with immaculate spelling and grammar, likewise the SPAG of any partial submission.
Might add that I have seen a lot of wannabe efforts, and many would be vastly improved by cutting/pruning unnecessary words/waffle.
My first published novel (for a minor publisher some years before I found an agent) started as a reject which I rewrote, with drastic cutting, for a competition asking for just the first 4000 words.
After such a major pruning, I wondered why I hadn’t done that in the first place! (My entry went on to win one of 6 x 2nd prizes - this was donkeys’ years ago though.)
I might add that I know a lot of authors and most had a lot of rejections before their ‘first’ novel was published.
Good luck and all the best.
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