Yes, though it's not a quick in-app edit. There's no way to change your first payment date directly once your plan is set up, so instead you cancel your current plan and set Split Pay up again with the new date.
The flow:
Cancel your current plan. In your Split Pay account, open your Plan Details and tap Cancel Plan. This also cancels the autopay to your landlord, so nothing goes out on the old date. (You can only cancel if you don't have an unpaid second Split Pay payment, so pay that first if it's still due, and you can't cancel once a payment has started processing.)
Set Split Pay up again, choosing your new first payment date.
Your landlord accepts the new autopay. Because you pay your landlord directly, setting up again creates a fresh autopay request they'll need to accept, just like the first time.
Keep in mind your new first payment still has to fall within the normal first-payment window, and until your landlord accepts, it isn't scheduled yet. For more on cancelling, see Can I cancel a scheduled direct payment to my landlord?