I would absolutely fight to get an L&D job right out of school, but big piece of advice: Not everywhere that decides to give you a shot is actually capable of giving you a real shot.
When you go into your interviews find out more about the hospitals: Are they private or county hospitals? Is it a teaching hospital? Have new grads been trained to their unit before? do they have a set system or a cohort of people who will go through it with you? do they have a nurse educator? Are they short-staffed/do people on the unit seem to be satisfied with management and have the resources they need to be successful?
My first shot at L&D was a bust because I took a job at a smaller private hospital without many resources, had an unsupportive preceptor and not a lot of others to turn to, in a hospital culture where being anything less than perfect was unacceptable.
I went to Postpartum for two years then ended up at a different hospital after that to try Labor and Delivery again. The new hospital I work at is night and day to my first job. It's a large county hospital, a teaching hospital where learning and asking questions are welcomed and making mistakes are just part of being human, something you grow from. I'm flourishing now when before I was drowning and constantly being told it was all my fault!
I wish I hadn't been so desperate for a job in L&D that I was willing to go anywhere. I wish I'd been able to see the first hospital I interviewed at wasn't going to be able to support me. I honestly feel like I didn't know what to look for though until I went through it: Go with a teaching hospital, somewhere that is used to new things/new faces. Somewhere where there are multiple layers of support for new grads and where new grads often go to get trained in L&D. You only get that foundation one time!
Switching into postpartum and doing that first was actually a really great way to learn nursing and be in a specialty that was close to what I wanted. I feel like Mother/Baby is kind of like the med-surg of women's health, prepared me well for the transition into L&D. That would be another good option for you, to start out there. It's a fairly common way to do things.
If not postpartum, I'd try for something OR, where you learn sterile techinique/timeouts/counts and other things that will also be something you have to do during a csection.