If you are an unknown author who just published your first book online and have done limited advertising but its a great book, how long can it take before the word will get around about your book?

Don’t wait. Build a social media channel: like an account on Instagram, Twitter, or Facebook. Work on it a little bit every day. The vast majority of your content should have to do with either the genre of your book or the subject matter. So if your book is about a ninja seamstress, post things about ninjas and seamstresses. Connect with other accounts that are focused on similar interests, and other people talking about books.
Word of mouth doesn’t just happen. You could write the greatest book in the history of the world and it wouldn’t sell on its merits alone. You’re going to feel cheap and pushy, but if you don’t market your book (and that doesn’t mean you need to buy advertising), then nobody is going to read it.
Make connections with actual people on whichever social media platform you decide to use (Facebook, Instagram, Twitter, etc.). Make friends with these people: repost some of their stuff consistently, and make sure it has to do with the theme or large parts of the subject matter of your book. And that doesn’t mean “she’s a woman, my book is about women, therefore that’s good enough”, I mean more specific categories than that. Is your book about a zombie teenage pregnancy? Well then go look for zombie girl stuff, and people talking about teen pregnancies, but with a positive spin.
Never go negative. Keep it light, keep it fun. Some amount of spilling your guts about a terrible car accident, break up, death in the family is OK, but use that very sparingly. People will get bored of your mopy, self-obsessed content very quickly, so remember that 99% of the content should be light and fun. You never see suicidally depressed car salesmen, or if you do, then they don’t show it.
I have no idea how long any of this will take, but a lot of it depends on you posting consistently, riding whatever trend is hot right now, and friending, following, commenting (positively), and “liking” a lot of other people’s content.