Hi, welcome to BYC!
First let me say that I wouldn't try to hatch FIRST eggs if she just started laying. The reproductive system is just getting up and running so they may have hiccups like double yolks or shell-less eggs. Which means you might hatch a bunch of deformities. Also note that IF she just started laying and is a pullet... her body and mind are still growing and maturing. I will NOT let my gals brood if they under a year old. It's like letting a teenager verses a lady in their mid 20's. Their bodies still need the nutrients from regular feeding which they don't do when sitting. My ladies usually lose some weight AND they become very shaky. Just not gonna let them lose condition like that on my watch. Once they become more mature, their bodies are much more filled in and better equipped to handle the situation, though it is still hard on them. And I often will adopt chicks from the feed store (up to 6 days old but younger is better) or from my incubator to the broody ladies so they don't sit for sooo long and I get to try other breeds that way... without having to deal with all the extra cockerels that come along with hatching. I'm ok with it now, but in the beginning butchering is difficult. And not all will be able to find homes. We knew we wanted to feed ourselves, so we committed... but some people won't be able able to. Sometimes they will keep a stag pen for all their boys to live in until their day comes naturally. I do keep a stag pen, but only for breeders or eaters... nobody stays forever and how long they do is often dictated by their behavior among the flock.
No matter how many eggs you do or don't leave in the nest... broody is a hormonal thing. I collect all eggs everyday and have some broody's that will sit on nothing but imagination. Yes some breeds are more likely than others to go broody.. though I see exceptions ALL the time. It, like so many other things can really vary by individual. I have one girl that goes broody EVERY 3 weeks like clock work until I let her sit. Or every 3rd egg once she breaks from her original broody spell.
If your gonna leave eggs in the nest, I suggest fake ones and collect the eggs you wish to hatch until you have someone actually broody. That way the hatching eggs won't be jostled every time someone enters or exits the nest. Less chance of breakage, scrambling, fecal contamination, or other things that make for less hatch-ability. IF and when you do set eggs, be sure they all go under on the same day. Have them marked well and check the nest daily to remove eggs that might have been deposited by other ladies.
I'm sure plenty have posted since I started typing.
I will add that there ARE a few things that DO encourage a broody IF they are going to.. adequate nutrition (not layer in my opinion & NOT "spoiled" by treats), plenty of space (no overcrowding), shelter, proper internal and external parasite control as needed, and protection from predators. Generally good health and an overall sense of well being. Even then some ladies don't have a broody bone in their body. And by providing adequately... broody is NOT seasonal for me the way it WOULD be in nature where the seasons predict how much resources are available. I live fairly far north, with about 8 hours of daylight in winter and no artificial supplementation... and I had broody's in the breaker MOST of the winter so far

and a girl who is a few weeks into raising a chick right now.
My broodiest are of course the Silkies. My French Black Copper Marans have also been plenty frustrating and even rehomed due to excessive broodiness. But I've had broody Swedish Flowers, and even hatchery barred rock (her second year she went broody even though she didn't in year 1) raise chicks. A local guy even got a rooster from me for his broody red sex link who hatched and raised a clutch of chicks there after. And seen broody leghorn, though it isn't their norm. When I first started with chickens I though getting a broody was rare and would never happen for me. Boy was I wrong! So I would say just enjoy your hobby and maybe let happen naturally as chicken math tries to wrangle you in.
And I will note that while it's cool to see a broody raise chicks... there is nothing friendly about them during most of that time, if you are used to them being lap pets. It is very much a blessing to witness... if all goes well.
Last but maybe not least... you won't get ANY eggs from a broody hen. In my experience it last between a minimum of 3 but up to 12 weeks. Not usually less than 7 with adopted chicks that didn't include 3 weeks of sitting before hatch.
Hope this is helpful to you!
And good luck in your future en devours.
