Who has custody when there's no court order yet?
Before any order exists, married parents generally have equal rights to their children, and neither one is violating anything by having them. Nobody is technically in the wrong, which is precisely what makes this period unstable and worth resolving quickly.
The arrangement you fall into now also tends to become the arrangement a court sees as working. That is the part to take seriously.
What "equal rights" means in practice
It means neither of you can point to a document. If one parent keeps the children and will not hand them over, there is often no order to enforce, and police will usually treat it as a civil matter and decline to intervene absent a safety concern.
That cuts both ways, and it is why the answer to a difficult co-parent right now is a court order rather than a confrontation.
If you were never married, the picture differs: custody rights generally run through parentage, and an unmarried father usually needs to establish it, either by a voluntary acknowledgment of paternity or by a court order, before he has enforceable rights. What the arrangement looks like in the meantime differs a good deal from state to state. Confirm this locally rather than assuming, because it varies more than almost anything else here.
The thing that actually matters
The status quo you create now is what the first order is likely to reflect.
Courts prefer stability for children, so an arrangement that has been running for a few months and appears to be working is one a judge is reluctant to disturb. That is sensible, and it is also how a temporary convenience becomes a permanent schedule. The temporary arrangement often decides the permanent one, and this period is where it starts.
So the practical advice is uncomfortable: agree something deliberate now, even informally, rather than drifting. If you want substantial time with your children, have substantial time with them starting immediately, and keep a record of it.
What not to do
Do not take the children and disappear. Moving them out of the area without notice, cutting off contact, or refusing to say where they are will be the first thing described at the first hearing, and it does more damage than whatever it was meant to achieve.
Do not leave and let the children stay by default if you want meaningful time. This is the most common regret. Moving out does not forfeit your ownership of the house, but it can quietly establish a parenting pattern.
Do not treat an informal arrangement as protection. It is not enforceable. If it stops working tomorrow, you have nothing to take to a court except an account of what used to happen.
Getting to something enforceable
Write down what you have agreed, even in a text message. It is not an order, but it evidences the arrangement and both parents' understanding of it.
Ask for temporary orders early. Once a case is filed, a court can put a schedule in place while everything else is worked out. This is the single most useful step available, and people delay it far longer than they should.
Keep a simple calendar of where the children actually were. Whoever ends up asking a court for something will be asked what the pattern has been, and the parent with a record answers better than the parent with an impression.
If you are leaving an unsafe situation
The above assumes two parents who are simply unresolved. If you are leaving because you are not safe, taking the children with you is a different question with different rules, and there are emergency procedures for it. Talk to an advocate before you go if you possibly can. The safety resources page has the numbers.
Default rights before an order, and what unmarried parents must do to establish them, vary substantially by state. This is one of the areas where a general answer is least reliable, so confirm yours with a licensed family-law attorney where you live.