I don't know if this varies by state, but I'll answer for my location.
The lawyer sets up your trust at the same time you make the will. That trust can be empty while you're alive, but it exists legally so you make it the beneficiary of your life insurance, your bank accounts, etc. you set up your real estate, if any, to transfer to the trust upon your death. The only thing you don't do that to is IRAs. Those beneficiaries are still the kids names.
The way my lawyer explained it, legally it as as if everything I own is mine while I'm alive and then, at the exact moment before I get hit by a truck, time pauses, and legally everything jumps into the trust and is controlled and distributed according to my trust's instructions.
edit to add - as a single parent, you also absolutely need to do the right paperwork for your medical decision-making and please don't just think about a will but also handle all the legal, financial, custody, etc issues for if you become incapacitated but still alive.