I am not sure how those not having read the book will take to the series. Some aspects/scenes - without knowing their background - might look too randomly strange. Like a series happily celebration it's own surrealism just for the sake of it.
I'm only two episodes in so far, and I'm watching along with someone who's read the book, but even without having read the source material myself I'm able to accept those turns toward the absurd/unprecedented/downright freaky on their own terms. It is a deeply weird show, which from my understanding is based on a similarly fantastical novel, but one need not be familiar with the aesthetic of the latter to appreciate the artistic choices made by the former.
I will say, though, that I am probably the most annoying person to watch a show with if you've read the source material and I haven't. Whenever something
really fucked-up happens--not just on this show, but also during the first five seasons of
Game of Thrones and whenever I'm watching something in the Marvel universe--I cannot resist asking if that's from the books or just the show-runners being weirdos for the sake of being weirdos. I do sense that
some of that show-runner tomfoolery is at play with
American Gods, but I couldn't say how much and at the end of the day it doesn't affect my enjoyment of the show one way or the other. In general, if there's a show or movie that falls somewhere on the sci-fi/fantasy spectrum, I have zero interest in reading the book(s) anyway; such novels tend to bore me, but engaging with the stories on-screen is usually a damn good time because I am unburdened with the trouble of knowing how well or how poorly the producers are adhering to the source material.
TL;DR:
American Gods is pretty cool but I am definitely the goddamn worst.